The Federal statute against false statements at 18 U.S.C. 1001 seems to ban almost any lie that gets reported to the executive or judicial branch (the legislative branch is treated more narrowly).
Example: Mary, a private citizen, lies to Jane, a private citizen. Jane believes Mary. Mary has no idea that Jane is going to contact an executive branch agency and does not ask her to. Jane reports the content of Mary's statement to an executive branch agency. Therefore, Mary is guilty. And, if Jane was not sure whether to believe Mary, both might be guilty.
Even if Mary and Jane only met in a private apartment house lobby and never saw each other before or after, Mary's lie was that a pterodactyl landed on her shoulder and gave her the keys to a new car, Jane reported on the pterodactyl to the National Park Service, and a Park Service ranger, using official office space and time, told her that pterodactyls have been extinct since before the first human was born, it was against the law for Mary to say what she said about a pterodactyl with car keys.
To make a starker example: The statute says "whoever . . . falsifies, conceals, or covers up by any trick, scheme, or device a material fact . . . shall be . . . imprisoned . . . .". Joe and Bob are standing on opposite sides of a state boundary. Joe tries to rob Bob at knife-point. Bob has money but it's in a pocket and thus Joe cannot see it. Joe believes that Bob has nothing and leaves. Bob reports the robbery attempt to the FBI (which has interstate jurisdiction) and the FBI questions Joe. Joe reports that he wanted to rob Bob but that he (Joe) couldn't see that Bob had money. Both are guilty: Joe for attempting a robbery and Bob for concealing from the intended robber that he (Bob) had money. At sentencing, Joe, under one state's law, for attempting the robbery, could get 4 years, while Bob, under Federal law, for concealing money from the intended robber and thus discouraging the robbery, could get 5.
By the way, had Bob carried his money openly in his hand and had Joe succeeded in robbing him, Bob would have been innocent and Joe the robber could have gotten 7 years, so the nation could have exacted less in total punishment for the successful robbery than for the awful crime of stuffing one's own money into one's own pocket and thereby foiling a robbery. Clearly, public policy favors robbery, and if Bob gets robbed he should rob Harry, who should rob me, just for starters.
If I try to imagine how to live daily life so as to conform to this statute, I don't know where to begin.
Seriously, what struck me about the statute is that it does not specify to whom the false statement must be made for it to violate the law. Usually, perjury statutes I've seen say that you can't lie to a government agency or officer or on a form you submit to a government agency. Section 1001 doesn't say that, even though it has been litigated and amended. Has the Federal judiciary confined the statute's reach? It may be Draconian and it may never have been enforced to this degree, but I don't think it's unconstitutional. For example, I wouldn't call it vague or overbroad.
Possibly of interest: When is it illegal to lie?