[Nero Germanicus]

That only applies if there was proof the child was born outside of the United States. The mother would have had to be 19 and Ann Dunham was four months shy of her 19th birthday. There is no age requirement for mothers giving birth within the US.

[MortMan]

That only applies if there was proof the child was born outside of the United States.

Exactly backwards. As with all proof of citizenship, it was incumbent on the citizen to prove their status, not for the government to disprove it. The correct way to state this is:

That only applies if there was no proof the child was born inside the United States.