No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President;.
The President is Commander in Chief of the Armed Forces.
For this reason, alligence MUST be to the US.
That is why they wrote in the distinction between Natural born Citizen, and regular Citizenship as bestowed by a Government.
0bama is not a Natural born Citizen