A lot of people successfully lied about their age to get in the army for WW2. Considering the whoppers so many people believed from Barack, I'm not going to rule out the possibility that his alleged father was also a talented prevaricator, just like the uncle who liberated Auschwitz.
He was big for his age.
While a number of 16- and 17-year-olds undoubtedly did, it's more than a bit of a stretch to think that an 8- or 9-year-old could possibly get away with it.