Can someone help me on this?

If for the sake of argument, Obama was born outside the USA to a natural born American mother and a Kenyan father, isn’t he still a natural-born US citizen for the purpose of qualification for the office of President?

I think of children of diplomatic personnel, military dependents that might have been born outside the USA and maybe the base did not have obstetric facilities, the baby was born at a local hospital, US citizens overseas for business purposes, tourists going into early labor, etc.

Maybe I don’t understand the rules.