Being ‘open to debate’ because some birthers are raising invalid objections to the standard and correct interpretation is a bit like saying the validity of capitalism is open to debate because there are some marxist profs out there.
Sure, but ... they’re wrong.
If you want to disprove the simple fact that “natural-born citizen” means something other than ‘citizenship at time of birth” show us the distinction in US law. You can’t.
So far as I know the phrase “natural-born citizen” does not appear at all in US statutes.
It does however appear in this Supreme Court decision:
1875 opinion of Supreme Court Chief Justice Waite in Minor v. Happersett
In his majority opinion stated: “The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that. At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.” Minor v. Happersett, 88 U.S. 162 (1875).
It seems to me the matter of Presidential eligibility is still legally undecided. It simply has never been explicitly addressed by Congress or the Supreme Court. SCOTUS had the chance in January 2009, and Chief Justice John Roberts reportedly was the missing 4th vote to hear the Obama case.