From that link:
Eligibility for office of President
According to the Constitution of the United States only natural born citizens are eligible to serve as President of the United States or as Vice President. The text of the Constitution does not define what is meant by natural born: in particular it does not specify whether there is any distinction to be made between persons whose citizenship is based on jus sanguinis (parentage) and those whose citizenship is based on jus soli (birthplace)
True. So everythng depends on the semantics of "natural born citizen." An issue for which the Constitutional authority to decide rests with the Supreme Court. Who decided in Minor that it means "born in the US to parents who were citizens."