You cite people saying BHO was born in Kenya and assume they must have learned this as a result of Obama making such a claim.
Apparently he told Lynn Sweet that he had a childhood in Kenya.
"Obama's next big international journey will be in 2007r--he's looking at China, India and Indonesia, ``where ironically I actually have more of a childhood than I do in Kenya.'' "
She went with him on that overseas trip, so I suspect she had a LOT of time to talk to him. Seems strange that she would have written down such a quote in error.
And you’ll note that BHO did not say he was born in Kenya.