Why would there be any doubt in your mind? Of course it was LBJ and J Edgar Hoover. Even a complete idiot can figure only those two could have pulled off the crime of the century.
It was done for the Domino Theory. All involved thought they were saving the US from the Soviet Union. It was a lot more than two guys cooking it up. LBJ and Bill Clinton are tied for the most corrupt presidents in US history, that came in handy in 1963 in LBJ's case when it was necessary to employ the lowest scum of society to take care of their problem.
They tricked Oswald to actually think he was an agent to end Castro's regime up until the very end when he realized there was a whole other operation going on and he was the patsy.
Oswald was a marine and deserves to have the facts looked at before the word "traitor" is directed his way. Even the House investigation concluded there was more than three shots. Again, search "Jim Braden".