True, but he cannot be president.
born to us citizens is natural-born.
True, but he cannot be president.
You are wrong in your assumptions.
Yes he can run for President, he is a U.S. citizen at birth, thereby a natural-born citizen. natural born citizen never meant 'born on U.S. soil only' it meant any individual born in the United States AND anyone born to U.S. Citizen parents abroad.