“Born to a single mother” would sort of invalidate the COLB that Obama has presented?
If SAD gave birth to what is known as BHO, Jr. without a father listed on the COLB, but born outside the U.S. he would not be a citizen because she was not old enough at the time to transfer citizenship to her child under the Immigration and Naturalisation Act of 1952.
In neither case would he be a "natural born U.S. citizen". (don't confuse with native born, natural born "American" citizen, or other legal weasel words)