How Congress defines naturalization for statutory purposes is immaterial when the question is a Constitutional one. In 1898 the SCOTUS made clear that the jus sanguinis was never part of our common law, and that persons born abroad and thus outside of U.S. jurisdiction are made citizens only through naturalization. That principle was affirmed by the Court in Rogers v. Bellei (1971). And the Scalia/Thomas concurrence in Miller v. Albright (1998) indicates the principle is still very much alive and well.
Congress can define naturalization so as to exempt that class of at-birth citizens from the procedural requirements of the naturalization laws. But that doesn't change how, from the Constitutional perspective, the grant of citizenship at birth to certain children born abroad to citizen parent(s) is considered an act of naturalization.
Though the argument you're making is the sort of thing a judge who is disinclined to interfere in the electoral process may seize upon as a way to work around Bellei.
Especially since 8 US Code 1401 also provides for the following, along with other sets of qualifying conditions for "citizen at birth":
The following shall be nationals and citizens of the United States at birth:
(a) a person born in the United States, and subject to the jurisdiction thereof;
Unless someone wants to argue that we area ALL naturalized citizens, he would be forced to argue that there are distinctions among the quality of citizenship granted by the statute, not merely among the qualification conditions for citizenship, that are simply not present in the statute.
I think either argument would lose if tested in a courtroom.