There was much confusion surrounding her answer, but it's clear that if BO was born in the village he wasn't born in Mombasa and vice versa. McRae used slight of hand to make contradictory non-evidence look like two pieces of corroborated evidence to those who wanted to believe.
Travel to Africa was harder and rarer in those days. And if you were BHO, Sr. would you really want to take your White wife to meet your other (African) wife and your angry father who probably didn't much care for Whites, as he didn't seem to like anybody very much?
The natural born citizen thing has to do with interpretations more than anything else. It's by no means certain that the founders intended their words to be understood as the theorists claim, and it's unlikely that the courts would support their interpretation today.