>>Yet some people seem intent on carving out some sort of third type of U.S. citizenship, besides that of either being “natural born” or “naturalized”. <<
It has already happened. That third type of citizenship is called “Kenyan” and is sufficient to hold the office of President of the United States.
Either he had U.S. citizenship conferred upon him at birth, or he is an illegal alien.
So still no exception. Obama is either a U.S. citizen by birth, or he would have had to be naturalized.
A naturalized citizen is not a natural born citizen. But are there citizens who were not naturalized who are also not natural born? Some say yes, I don't see where there is any sort of third type of citizenship spelled out in the law.