You’re right bc in 1963 any involvement of the FBI/CIA would have come as a real shock to the American people. But then you had Mark Felt, Asst. FBI Director who brought down Nixon as Deep Throat; you had the hiding of the Hunter Biden Laptop by the FBI from its receipt in December 2019 which polls indicate if it had been publicized and was known to be authentic, Trump would still be President. So its not too far a stretch to think they may have been even more directly involved in the removal of a President in 1963 under LBJ’s close friend and long-time ally, J Edgar Hoover.
They probably were behind the Reagan assassination attempt as well. Don’t forget that the shooter’s family was good friends with the Bush family!