If Obama was born on US soil to Stanley Ann, and if Obama Sr. was indeed his birth father, he's a US Citizen.
He is NOT, however, a Natural Born (US) Citizen, per the Framers' understanding of that term. He would need to have been born to two US citizen parents on US soil to meet the definition.
Oh, so dependents of servicemen born in foreign hospitals don't qualify??? Does John McCain being born in the Panama Canal Zone qualify?
Now then, in the case of The Won, the official narrative is that he was born to Stanley Durham and BHO (Senior)-- in Hawaii. But BHO (Senior) was not a citizen at that time. Therefore, that would be a prima facie case that The Won is not constitutionally qualified to be President under your definition. Yet Mrs. Clinton's campaign refused to try to make this case. And...it would mean that the Birth Certificate would be irrelevant.
Here's one for you fantatics on this: What if you don't know who the father is? Suppose a U.S. Citizen gives birth on U.S. soil-- but doesn't know the citizenship of the child's father? Does the Consitution forbid a bastard of unknown progeny to become President?