By your logic, someone born in the US also is granted his citizenship by the same law. Or did you fail to notice:
A. General Requirements for Acquisition of Citizenship at Birth
A person born in the United States who is subject to the jurisdiction of the United States is a U.S. citizen at birth, to include a person born to a member of an Indian, Eskimo, Aleutian, or other aboriginal tribe.
So since both being born in the US and being born to a citizen outside of the US are covered by the same law, I guess there is no such thing as a "natural born citizen".
What I noticed, and what you've either failed to notice or have chosen to ignore, is that it all falls back to U.S. Code: Title 8 - ALIENS AND NATIONALITY
So, NO, someone born in the US is NOT granted his citizenship by the same law unless one, or both, of his parents is a frigging ALIEN!!!