Obama appears to have asserted in his own biography that he was born in Kenya.
In a bio submitted for a 1991 booklet he wrote, he, or his literary agent, claimed he was born in Kenya. It’s hard to imagine that the biography was submitted without Obama’s knowledge.
If you observe Obama’s ease and eagerness to draw out and inflate meaning of aspects of his ancestry, you can begin to see how this biographical slip occurred.
In short, it suited Obama’s need for authenticity to pick up the family story of a Kenyan birth. He may not have known the truth one way or the other.