8 US Code 1401 provides for the following, along with several other sets of possible 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;
So, we're ALL naturalized citizens now?
Mind you, this is precisely the same section of the US Code that defines certain children of an American citizen born abroad as a US citizen at birth; it's merely a different qualification standard among several. There is no distinction made regarding the quality of the citizenship at birth granted.
A person born in the United States, and subject to the jurisdiction thereof does not depend upon the statute for their citizenship.