I don't think for a moment that they aren't powerful enough to have done the hit. I think they aren't powerful enough to control a whole bunch of other closely related stuff both during and after the operation. That is, stuff relating to the FBI, the CIA, and the Warren Commission. I think the Mafia was part of the operation all right, but that they were not acting alone.

The Mafia has often acted in concert with the CIA on various operations.