Born in the Philippines instead of Hawaii? Conceivable, and if true it would mean that he was not a U.S. citizen at birth and thus is not eligible to become president.
But there is no way that his mother is anyone other than Ann Dunham, since Obama is a dead ringer for Ann Dunham’s father when he was in his 30s.
I think he’d still be eligible if his mother was a US citizen, even if he were born in the Phillipines. But maybe the birth certificate leaves off the name of the mother, or misspells it, or has some other ambiguity on that point.
Or maybe the birth certificate doesn’t exist.
Maybe the story that he was born in Hawaii was concocted because he discovered that birth certificates are not public documents in Hawaii.