Having the likes of Allen Dulles and Richard Helms on the Warren Commission was the equivalent of having Katie Hobbs remaining as Secretary of State overseeing a gubernatorial election where she was a candidate. The players may change and the specifics will be different, but at the end of the day, the people in power will fix the results to suit their goals.
Gerald Ford was on one of those committees. He wrote an article for Popular Mechanics on what proof they had that Oswald did the shooting. A thread matching Oswald’s shirt was found stuck to the rifle butt plate.
It looks like Helms was not on the Warren Commission - he was only a witness.