The particular law in effect at the time Obama appears to have been born served to prevent the return to the USA of out of wedlock children born to American girls sent abroad by their parents to Catholic or Orthodox convents. That left the control of those babies to church authorities.
The law was later changed.
There are undoubtedly some court cases that deal with such matters although I don't recall any Freepers digging them up.
1. Dad was born in Kenya, a British subject...
2. Mom was not older enough to claim him as an American BORN citizen...
There are an number of referenced cases and a law timeline here.