Yep. I doubt JFK would have given a nod to this. That's probably the reason the CIA got rid of him.
Kennedy authorized the coup, the only thing he was naive about was he believed that Diem and his brother Nhu would be allowed to leave the country in exile. The one who really had it out for Diem was Averell Harriman who spent months coaxing Kennedy into plotting his overthrow.
Actually my money is on the Mob and CIA taking JFK out over the Bay of Pigs fiasco.