[El Gato]

And he's also a U.S. citizen from birth, which means he is a natural-born citizen

And their is your implicit assumption, for which there is no support in law or the Constitution. The Constitution does about 3 forms of citizenship. Art I, section 8 talks about naturalization, as does the 14th amendment. Art. II Section 1, speaks of Natural Born Citizen, and finally the 14th amendment speaks to "citizenship by birth in the US".

As I said above, the statutes make a person born outside the US, a "citizen at birth" under some circumstances. Such a person can hardly fit the 14th amendment definition of "(native) born in the US", but since Congress only has power over naturalization rules, they must be considered, for Constitutional purposes at least, "naturalized at birth".

[Non-Sequitur]

And their is your implicit assumption, for which there is no support in law or the Constitution. The Constitution does about 3 forms of citizenship. Art I, section 8 talks about naturalization, as does the 14th amendment. Art. II Section 1, speaks of Natural Born Citizen, and finally the 14th amendment speaks to "citizenship by birth in the US".

Then what defines the difference between citizen by birth and natural-born citizen?