Maybe he is. Maybe he isn't.
No court has ever ruled on exactly what "natural born citizen" means.
Being born on US soil might suffice. Having citizen parents might suffice.
Me? I think you need both...
Patrick Leahy, Hillary Clinton, Clair McGaskill, Barack Obama, trying to insure that John McCain was treated as eligible (he wasn't) so that the Republicans wouldn't dare raise the issue of Obama’s reputed father, signed Senate Res 511, where “born of citizen parents” was repeated again and again. There were at least two other resolutions. The Republicans were trapped by the media, who made McCain a pretend favorite, and Dems who generously held hearings to say, in effect, how unfair it would be if former POW, and McCain-Feingold sponsor couldn't run just because of an antiquated document called the constitution. There have been at least 24 attempts to amend Article II natural born, some only a few years old. It was not changed so the most effective policy, when someone you want to run for president is ineligible, is to pretend the founders didn't mean what they said, or quote those who want to change it but can't find the votes. That is the clever ploy used by Obama to put the criterion right out in the open where it wouldn't occur to most that there was anything wrong.
But you can bet our lawmakers knew, and our courts knew, even Ginsberg, who heard a case in 2001 where the definition was spelled out for her, and not challenged. Our originalist justices know, and most judges know, even Michael Chertoff, who repeated the jus languinis - both parents citizens - requirement when commenting on the record about Senate Res. 511.