As a matter of constitutional law, natural-born citizen is kind of undefined. If he had been born outside the US, the would have had dual or even triple citizenship at birth which would seemingly also qualify.
Right...undecided in courts, but my (naive) reading of it would mean that you have to be a citizen from the moment you leave the birth canal. It doesn't seem like it should matter where exactly you were born...if your American parents were vacationing in Bermuda for 1 week when you were born prematurely, that means you can't run for president 35+ years later?
Ted Cruz, a Canadian, was almost nominated as the Replubican candidate. Clearly, a large number of people feel that the definition of natural American citizen is a bit more flexible then that.