Respectfully, the concept of natural born citizen goes back WAY farther than the birth of the US. Or the birth of England. Even before the birth of Rome.
Why does that matter? Because our Founders were well read and based their language on an expectation that those who would interpret it would be similarly well read.
Sadly, they were mistaken. Sigh.
/not a dig on you, a dig on our failed “education” system.
Oh, de that whole Jus Sanguinis (of the blood) thing, it really does go back a bit: http://www.lamblion.us/2008/08/those-boring-begats.html?m=1