Well, there sure is some interesting case law here. I don't know all the facts in this specific allegation so will withold comment. However teh below is from Wikipedia.
US Supreme Court cases relating to citizenship, generally
Although the U.S. Supreme Court has never specifically addressed the meaning of "natural born citizen," there are several Supreme Court decisions that help define citizenship:
Dred Scott v. Sandford, 60 U.S. 393 (1857): In regard to the "natural born citizen" clause, the dissent states that it is acquired by place of birth (jus soli), not through blood or lineage (jus sanguinis): "The first section of the second article of the Constitution uses the language, 'a natural-born citizen.' It thus assumes that citizenship may be acquired by birth. Undoubtedly, this language of the Constitution was used in reference to that principle of public law, well understood in this country at the time of the adoption of the Constitution, which referred citizenship to the place of birth." (Much of the majority opinion in this case was overturned by the 14th Amendment in 1868.)
United States v. Wong Kim Ark, 169 U.S. 649 (1898): A person born within the jurisdiction of the U.S. to non-citizens who "are not employed in any diplomatic or official capacity" is automatically a citizen.
Weedin v. Chin Bow, 274 U.S. 657 (1927): A child born outside the U.S. cannot claim U.S. citizenship by birth through a U.S. citizen parent who had never lived in the U.S. prior to the child's birth. (This is still true today, although the specific statutes upon which the Supreme Court's ruling was based have changed since 1927.)
Montana v. Kennedy, 366 U.S. 308 (1961): A person born in 1906, whose mother was a native-born citizen of the United States and whose father was a foreign citizen, who was born overseas and then moved to the United States, was not a citizen of the United States by birth. (Note that the relevant laws have changed considerably since 1906, so this decision does not necessarily apply to later cases.)
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