Why do you think it would be impossible? His mother traveled around the world and his father is Kenyan....
Because Kenya had no international airport in 1961 and it took two and a half days to fly from Nairobi to Hawaii.. Further, pregnant women didn't fly after the second trimester... or for 6 weeks after birth.
If Obama had been born in Kenya his birth would have been registered at the nearest US consulate or, at the British Embassy for British East Africa. That's the way it was done for US citizens born abroad.
Plus, his mother never traveled outside the US until her second marriage. Which also means Obama has had a US Passport since he was 6 or 7. Its just gross ignorance. Indonesia doesn't allow for dual citizenship.