Want to site some case law for that?
Article 2, section 1 of the Constitution states, “No person except a natural born citizen, or a citizen of the United States at the time of the adoption of this Constitution, shall be eligible to the office of president; neither shall any person be eligible who shall not attained to the age of thirty-five years, and been fourteen years a resident within the United Satates.”
The addition of a grandfather clause in this paragraph says a lot as to the meaning of natural born. The first thing it says is that being born in the US is not enough to be natural born, otherwise the grandfather clause would not be necessary. The writers and delegates, having been born in the US, wanted to be eligible for the presidency, but most were the children of British subjects. Knowing that that eliminated them from being natural born and, thus, from eligibility, they included the grandfather clause which expired when the last person alive at the time of the ratification of the Constitution died. So, being a native born citizen is not the same as being natural born. If it were the framers would not have included the clause.
When asked to define natural born citizen, John Bingham, the author of the 14th ammendment which extended the bill of rights to former slaves, stated, “Any human born to parents who are US citizens and are under no other jurisdiction or authority.” The Naturalization Act of 1790, also passed by this congress, declared “And the children of citizens of the US shall be considered as natural born, provided that the right of citizenship shall not descend to persons whose fathers have never been a resident of the US.” Neither of these definitions, one from US law, mentions birthplace, only the parents’ citizenship.
This concept of citizenship by blood as opposed to citizenship by geography is a concept with a long history in British common law. A law passed in 1677 says that natural born citizens are those persons born to British citizens, including those born overseas. Alexander Porter wrote an article over 100 years ago in which he declares that the framers drew upon this difference in the law of heredity and territorial allegiance to define a third class of citizen applicable only to the eligibility to hold the office of president. According to Morse, “the framers thought it wise to provide that the president should at least be the child of citizens owing allegiance only to the US at the time of birth.” He goes on to say that the the eligibility of the president “was scarcely intended to bar the children of American citizens, whether born at sea or in foreign territory.”