I wonder how the fact that it was a bigamous marriage might affect things? Although it seems that Stanley Anne did not know that BHO Sr. was already married when she married him.
That same link says if the birth is out of wedlock ...
A person born abroad out-of-wedlock to a U.S. citizen mother may acquire U.S. citizenship under Section 309(c) of the INA if the mother was a U.S. citizen at the time of the person's birth and if the mother was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the person's birth. The mother must be genetically related to the person in order to transmit U.S. citizenship.
Some anti-birthers will argue that the fact he is a citizen at birth makes him a natural born citizen; others make a distinction that citizenship is conferred by statute, rather than by a judicial decision (Wong Kim Ark); giving the courts the power to define Natural Born Citizen however they decide, but not allowing Congress the same power.