In 2007 my wife and I took the 15yo daughter of a friend with us to Brazil. I investigated the US angle on this and at the time there was no rule I could find.
As it turned out, nobody cared a whit about who she was or who we were in relation to her, in US airports.
In contrast, my 15yo nephew, who was on the same trip, is Brazilian and his travel is restricted by Brazilian laws. Whenever we go to Rio with just his mother (my SIL), we need to get a special letter from the consulate in NY giving him permission to travel alone with his mother. And they always check the letter in the airport at Rio before letting us all come home.
On that particular trip, they first scrutinized my nephew’s letter carefully and then looked at our friend’s daughter, asking her “Do you speak Portuguese? You’re Brazilian. Where is your letter?” at which point we had to work hard to convince them she wasn’t Brazilian. To be honest, she looks amazingly Brazilian, but there is no connection whatsoever. Once they understood she was an American citizen only, they simply waved us on without any concern about whose daughter she was.