If that were true, there would be no such thing as a "natural born citizen." Which would make the Constitution and its requirements ridiculous.
I'm a natural born citizen. I was born in Omaha, Ne., to two citizen parents. All of my people have been in this country for more than one hundred and fifty years, and the majority of them have been here for three to four hundred years. The framers of our Constitution pegged my qualifications for the presidency to that natural set of facts, not to the subsequent immigration and naturalization statutes passed by Congress.
Seven U.S. Presidents had one or both parents who were not born here.
http://www.presidentsparents.com/presidents-born-outside-usa.html