Honestly, I have always thought that the birth certificate thing was that BO’s parents never married and he was a bastard. And he was too thin-skinned to deal with it.
BO is a still the poor little boy whose parents both abandoned him. If you view him through that lens, a lot of what he does makes sense. Not good for the country, but it does explain him and his actions.
My opinion only.
That is one possibility. It may also be that the father’s name was not provided and listed as “UNKNOWN.”