I believe the Foreign Affairs Manual may be referring to the idea that under international law, the nationality of the natives of a territory becomes that of the United States when the United States acquires sovereignty over the territory. Thus, when Congress authorizes the acquisition of territory, it may be considered that Congress implicitly acquiesces to this principle—but has the right to override it, since there does not appear to be a constitutional right to non-citizen nationality. Here are some examples of when the Supreme Court appeared to endorse this unwritten principle:
Inglis v. Trustees of Sailor's Snug Harbor, 28 U.S. 99, 136 (1830) (Johnson, J., concurring):
[...] the demandant owed allegiance to the king of Great Britain, as of his province of New York. By the revolution that allegiance was transferred to the state [...]
Boyd v. Nebraska ex rel. Thayer, 143 U.S. 135, 162–163 (1892):
Manifestly the nationality of the inhabitants of territory acquired by conquest or cession becomes that of the government under whose dominion they pass, subject to the right of election on their part to retain their former nationality by removal or otherwise as may be provided.
All white persons or persons of European descent who were born in any of the colonies, or resided or had been adopted there, before 1776, and had adhered to the cause of independence up to July 4, 1776, were by the declaration invested with the privileges of citizenship. [...]
Downes v. Bidwell, 182 U.S. 244, 369 (1901) (Fuller, J., dissenting):
Doubtless the subjects of the former sovereign are brought by the transfer under the protection of the acquiring power, and are so far forth impressed with its nationality, but it does not follow that they necessarily acquire the full status of citizens.
Fourteen Diamond Rings v. United States, 183 U.S. 176, 179 (1901):
The Philippines thereby ceased, in the language of the treaty, "to be Spanish." Ceasing to be Spanish, they ceased to be foreign country. They came under the complete and absolute sovereignty and dominion of the United States, and so became territory of the United States over which civil government could be established. The result was the same although there was no stipulation that the native inhabitants should be incorporated into the body politic, and none securing to them the right to choose their nationality. Their allegiance became due to the United States and they became entitled to its protection.
Gonzales v. Williams, 192 U.S. 1, 9–10 (1904):
By the constitution of the Spanish monarchy, and the Spanish Civil Code, in force in Porto Rico when the treaty was proclaimed, persons born in Spanish territory were declared to be Spaniards, but Porto Ricans who were not natives of the Peninsula, remaining in Porto Rico, could not, according to the terms of the treaty, elect to retain their allegiance to Spain. By the cession their allegiance became due to the United States, which was in possession and had assumed the government, and they became entitled to its protection. The nationality of the island became American instead of Spanish, and by the treaty, Peninsulars, not deciding to preserve their allegiance to Spain, were to be "held to have renounced it and to have adopted the nationality of the territory in which they may reside."
Dorr v. United States, 195 U.S. 138, 141 (1904) (citing American Insurance Co. v. Canter, 1 Pet. 511, 542):
[...] If it be ceded by the treaty, the acquisition is confirmed, and the ceded territory becomes a part of the nation to which it is annexed, either on the terms stipulated in the treaty of cession, or on such as its new master shall impose. On such transfer of territory it has never been held that the relations of the inhabitants with each other undergo any change. Their relations with their former sovereign are dissolved and new relations are created between them and the government which has acquired their territory. The same act which transfers their country transfers the allegiance of those who remain in it; [...]
It appears that the acquisition of U.S. nationality by cession or conquest was usually considered to apply only to the nationals of the state that previously had sovereignty. The Supreme Court appeared to say otherwise in Boyd, but perhaps this is a special rule for the American Revolution. The idea that third-country nationals would implicitly become U.S. nationals appears to be contradicted by Dorr, in which it was stated that "the relations of the inhabitants with each other" don't change.
The Foreign Affairs Manual states that "Persons born in the Canal Zone of alien parents did not acquire U.S. nationality at birth." (8 FAM 302.7-3(e)). Thus, the State Department's position appears to be consistent with the principle of transfer of nationality described above, together with the obvious fact that a person born in U.S. territory to parents who are U.S. nationals would be a U.S. national at birth. Birth in U.S. territory alone is not sufficient to confer U.S. nationality except where such nationality at birth has been explicitly granted by Congress (as has been done in the case of all current unincorporated territories that are inhabited).
Addendum: In Wong Kim Ark, the Supreme Court considered the Citizenship Clause to have codified the pre-existing common law principle that birth under the protection of a sovereign creates a bond of permanent allegiance (that is, nationality). Based on that principle, it is arguable that birth in an unincorporated U.S. territory (regardless of the parents' nationalities) should attract U.S. nationality (though not as a matter of constitutional right, per the Insular Cases). If this was indeed the operative common law at the time that the Canal Zone was created, all individuals born in the Canal Zone (other than those possessing diplomatic immunity) should have been considered U.S. nationals at birth until such common law was abrogated by the Nationality Act of 1940 (which would then have applied only to future births). The Supreme Court does not appear to have had the occasion to consider this argument, though it's not totally impossible that such an occasion could still arise.
