1. Dad was born in Kenya, a British subject...
2. Mom was not older enough to claim him as an American BORN citizen...
If you look carefully that law was written under the assumption that the mother had been born to foreign born parents (British, Italian or Greek subjects), and that she, herself, might well have been born abroad.
That law has been changed. I'm guessing that if there's been any case law on the matter the girl won.