His mother was not old enough at the time of Barry’s birth to convey citizenship on him.
If he was born in Hawaii, he is automatically a citizen regardless of who his mother or father was. Birthright citizenship via jus solis.
The law is different now than it was in the early 1960s.
I prefer the theory where his grandfather Dunham impregnated one of Barrack Sr's sisters. Under East African polygamist tradition that'd make Barrack Sr. the child's father since he was the eldest son in the family.
That would eliminate the rather arduous plane trip for Stanley Ann from Hawaii to Kenya.
His daddy was though.
Thanks for pointing that out early.