If he became a citizen because of the naturalization act he is a naturalized citizen.
“If he became a citizen because of the naturalization act he is a naturalized citizen.”
A naturalization act does more than naturalize citizens. It describes who needs to be naturalized, who does not, and how naturalization will take place.
The first act of naturalization was enacted in 1790, just 18 months after the ratifying of the Constitution. It specifically provided that “natural born citizenship” would apply to children of citizens born abroad.
My point in noting this law which no longer has any force is that it contradicts your oversimplified theory.