That may well be but it was the operating theory at the time of the writing of the Constitution. The meaning of the term "natural born citizen" must be understood by the legal meanings at the time of its drafting, not by modern political theories. This was the whole point of the late Justice Scalia's insistence of originalism when interpreting the Constitution.
Scalia seems to have been a texualist rather than originalist.
I’m not sure there are any originalists in today’s legal system.