Can you think of any plausible reason why O Sr would say Jr was born in Honolulu if he weren’t?
I certainly can.
Money. Barack Obama Senior was dead broke at the time. His life back home in Kenya was a shambles. He was walking with a cane during the 1971 visit because he had been involved in a car crash caused by his own excessive drinking.
He would sign any papers or make any statement they asked of him in exchange for money.