There is another exception to search and seizure which applies to places like airports and border crossings and entry to secured areas. See, e.g., United States v. Martinez-Fuerte, 428 U.S. 543, 545, 562, 566 (1976) (fixed immigration checkpoints near the border) and United States v. Mendenhall, 100 S. Ct. 1870 (1980) (airport search by DEA). But see, Reid v. Georgia, 100 S. Ct. 2752 (1980) (reasonable suspicion required when passengers had left the airport terminal and were about to board ground transportation).
These searches do not require a reasonable suspicion or a warrant. The legal theory is basically that in these places, there are routine checkpoints, and reasonable people know in advance that they may be subject to suspicionless searches.
The modern state of the law is spelled out at length in United States v. Aukai, 440 F.3d 1168 (9th Cir. 2007):
The Fourth Amendment requires the government to respect “[t]he right
of the people to be secure in their persons and effects, against
unreasonable searches and seizures.” U.S. Const. amend. IV. “A search
or seizure is ordinarily unreasonable in the absence of individualized
suspicion of wrongdoing. While such suspicion is not an
‘irreducible’ component of reasonableness, [the Supreme Court has]
recognized only limited circumstances in which the usual rule does not
apply.” City of Indianapolis v. Edmond, 531 U.S. 32, 37, 121 S.Ct.
447, 148 L.Ed.2d 333 (2000) (citations omitted). However, “where the
risk to public safety is substantial and real, blanket suspicionless
searches calibrated to the risk may rank as ‘reasonable’-for example,
searches now routine at airports and at entrances to courts and other
official buildings.” Chandler v. Miller, 520 U.S. 305, 323, 117
S.Ct. 1295, 137 L.Ed.2d 513 (1997) (holding Georgia's requirement that
candidates for state office pass a drug test did not fit within this
exception) (citing Nat'l Treasury Employees Union v. Von Raab, 489
U.S. 656, 674-76 & n. 3, 109 S.Ct. 1384, 103 L.Ed.2d 685 (1989)
(upholding warrantless drug testing of employees applying for
promotion to positions involving drug interdiction)). Thus, “where a
Fourth Amendment intrusion serves special governmental needs, beyond
the normal need for law enforcement, it is necessary to balance the
individual's privacy expectations against the Government's interests
to determine whether it is impractical to require a warrant or some
level of individualized suspicion in the particular context.” Von
Raab, 489 U.S. at 665-66, 109 S.Ct. 1384.
Under this rationale the Supreme Court has repeatedly upheld the
constitutionality of so-called “administrative searches.” In New York
v. Burger, 482 U.S. 691, 107 S.Ct. 2636, 96 L.Ed.2d 601 (1987), the
Supreme Court upheld the warrantless search of a junkyard's records,
permits, and vehicles. The Supreme Court reasoned: “Because the owner
or operator of commercial premises in a ‘closely regulated’ industry
has a reduced expectation of privacy, the warrant and probable-cause
requirements, which fulfill the traditional Fourth Amendment standard
of reasonableness for a government search have lessened application ․”
Id. at 702, 107 S.Ct. 2636 (internal citation omitted). Thus, New York's interest in regulating the junkyard industry, in light of the
rise of motor-theft and comprehensive motor vehicle insurance
premiums, served as a “special need” allowing inspection without a
warrant. Id. at 708-09, 107 S.Ct. 2636; see also id. at 702, 107
S.Ct. 2636. The regulatory statute also provided a “constitutionally
adequate substitute for a warrant” because the statute informed
junkyard operators that inspections would be made on a regular basis
and limited the discretion of inspecting officers. Id. at 711, 107
S.Ct. 2636.
In Michigan Department of State Police v. Sitz, 496 U.S. 444, 110
S.Ct. 2481, 110 L.Ed.2d 412 (1990), Sitz challenged the
constitutionality of suspicionless sobriety checkpoints conducted on
Michigan's highways, contending that the program violated the Fourth
Amendment's protection against unreasonable seizures. Id. at 447-48,
110 S.Ct. 2481. The Supreme Court upheld the sobriety checkpoints
because “the balance of the State's interest in preventing drunken
driving, the extent to which [the sobriety checkpoints] can reasonably
be said to advance that interest, and the degree of intrusion upon
individual motorists who are briefly stopped, weighs in favor of”
finding the sobriety checkpoints constitutionally reasonable. Id. at
455, 110 S.Ct. 2481.
Significantly, the Supreme Court has held that the constitutionality
of administrative searches is not dependent upon consent. In United
States v. Biswell, 406 U.S. 311, 92 S.Ct. 1593, 32 L.Ed.2d 87 (1972),
the Supreme Court upheld the warrantless search of a pawn shop owner's
gun storeroom. The search was authorized by a federal gun control
statute. The Court held that, “[i]n the context of a regulatory
inspection system of business premises that is carefully limited in
time, place, and scope, the legality of the search depends not on
consent but on the authority of a valid statute.” 3 Id. at 315, 92
S.Ct. 1593. Thus, “[w]hen a[gun] dealer chooses to engage in this
pervasively regulated business and to accept a federal license, he
does so with the knowledge that his business records, firearms, and
ammunition will be subject to effective inspection.” Id. at 316, 92
S.Ct. 1593.
We have held that airport screening searches, like the one at issue
here, are constitutionally reasonable administrative searches because
they are “conducted as part of a general regulatory scheme in
furtherance of an administrative purpose, namely, to prevent the
carrying of weapons or explosives aboard aircraft, and thereby to
prevent hijackings.” United States v. Davis, 482 F.2d 893, 908 (9th
Cir.1973); see also United States v. Hartwell, 436 F.3d 174, 178 (3d
Cir.), cert. denied, 549 U.S. 945, 127 S.Ct. 111, 166 L.Ed.2d 255
(2006);[United States v.] Marquez, 410 F.3d [612 9th Cir. 2005] at 616 [(as amended)]. Our case law, however, has
erroneously suggested that the reasonableness of airport screening
searches is dependent upon consent, either ongoing consent or
irrevocable implied consent.
The constitutionality of an airport screening search, however, does
not depend on consent, see Biswell, 406 U.S. at 315, 92 S.Ct. 1593,
and requiring that a potential passenger be allowed to revoke consent
to an ongoing airport security search makes little sense in a
post-9/11 world. Such a rule would afford terrorists multiple
opportunities to attempt to penetrate airport security by “electing
not to fly” on the cusp of detection until a vulnerable portal is
found. This rule would also allow terrorists a low-cost method of
detecting systematic vulnerabilities in airport security, knowledge
that could be extremely valuable in planning future attacks. Likewise,
given that consent is not required, it makes little sense to predicate
the reasonableness of an administrative airport screening search on an
irrevocable implied consent theory. Rather, where an airport screening
search is otherwise reasonable and conducted pursuant to statutory
authority, 49 U.S.C. § 44901, all that is required is the passenger's
election to attempt entry into the secured area of an airport. See
Biswell, 406 U.S. at 315, 92 S.Ct. 1593; 49 C.F.R. § 1540.107. Under
current TSA regulations and procedures, that election occurs when a
prospective passenger walks through the magnetometer or places items
on the conveyor belt of the x-ray machine. The record establishes that
Aukai elected to attempt entry into the posted secured area of
Honolulu International Airport when he walked through the
magnetometer, thereby subjecting himself to the airport screening
process.
A few of things made the situation in the Atlanta news report in the question are notable:
There was a very well paid informant who was working for the airline, rather than an attempt to get that information through normal official channels. Allowing someone to personally benefit from providing information that could have been obtained for free through an official channel or a new regulation was questionable from a waste of public funds and corruption angle. The tens of thousands of dollars of fees that the airline informant was being paid for providing tips to the DEA were excessive relative to the employee's compensation from the airline employee job that provided the employee with access to the information provided, despite not involving any actions that put the informant in peril or requiring the informant to meaningfully go under cover.
The DEA was engaged in civil forfeiture of not just drugs but of cash, with dramatically reduced due process protections, without evidence that the cash was necessarily connected to illegal conduct (and in some cases, in domestic flights, where it didn't have to be declared for customs purposes). Even in cases where a civil forfeiture of cash is based upon an illegal failure to declare that you had cash, without proof that it is connected to a crime, this poses an 8th Amendment "excessive fines" concern. See Timbs v. Indiana, 586 U.S. 146 (2019) (the value of vehicle seized far exceeded the maximum possible fine for the offense, and the fine actually imposed in the parallel criminal proceeding, and was allowed over the objection of the trial court judge in the criminal case, violating the 8th Amendment excessive fines clause). As the story linked in the question notes:
Traveling domestically with any amount of currency is legal in the
U.S.; only international travelers are required to declare carrying
$10,000 or more in currency.
The lack of due process protection associated with civil forfeitures is particularly concerning when the law enforcement agency and informant conducting the civil forfeiture often receive some or all of the cash collected in the forfeiture, destroying their neutrality with this financial conflict of interest.
The basis upon which the DEA decided to make the searches were not grounds that would have otherwise been the basis of valid searches outside the airport (basically, people with one way tickets were targeted and/or carrying cash on domestic flights and/or carrying legal amounts of cash on international flights).
While the seizures took place in the secured area of an airport where suspicionless searchers are permitted, it didn't advance the public safety concerns associated with normal TSA searchers, and the program was kept secret from the public unlike normal administrative searches. Indeed, the apparently DEA mostly claimed to be relying on "consent" to validate its searches rather than the administrative search exception to the 4th Amendment, even though not all of its searches were conducted with passenger consent.
These concerns resulted in the discontinuation of the program for political reasons, rather than due to a court order that the conduct was unconstitutional. But the controversy has more to do with the ongoing debate over the legitimacy of civil forfeitures and corruption, than it did with the narrow 4th Amendment search validity, although there is a colorable argument that this search was beyond the intended scope of the administrative search exception for airport searches, which were primarily justified "to prevent hijackings".
But the administrative search exception in this case was denying any remedy at all to innocent travelers who were searched and did not experience a seizure, and placed a huge procedural and legal fee burden on travelers who had cash seized in a civil forfeiture without any legitimate suspicion that the cash was related to in a crime. Even if a passenger hired a lawyer and prevailed in getting your cash back in a civil forfeiture proceeding, the passenger was deprived of the cash for an extended period of time and was also worse off for having to pay legal fees and to devote time and worry to the civil forfeiture case for no legitimate reason.