We saw a documentary last week that said the CIA embedded one of their own as a member of the Warren Commission. (The guy’s name was given, but I don’t recall it now.) They had to make sure things didn’t get out of hand and wanted to ensure misdirection away from the truth.
Allen Dulles was formerly head of the CIA, fired by JFK after the Bay of Pigs, and was on the Warren Commission. They were skilled at diverting the truth; thus, LBJ always told them to be careful of the Russian connection (where have we heard that before?) bc it might start a nuclear war. The real connection was to LBJ and his cohorts in the Deep State, period.