To elaborate on this a bit more, LBJ needed cover. If he had pols on both sides saying there DEFINITELY WAS NOT A CONSPIRACY he would be golden.
How did he do this? He used the CIA/FBI for what they are really good at.
And that is making it look like Russia did it.
By selling the story that if the fact got out that Russia was behind it, the US public would DEMAND nuclear war, he got everyone from both sides on board.
There’s a small problem with that theory:
Ion Mihai Pacepa verified that the USSR had conducted Operation Dragon, a KGB disinformation campaign, immediately after the JFK assassination (and he’d know because he was personally involved in planning the operation), and there’s at least one East German spymaster who directed someone to ask Fidel Castro about the JFK assassination when asked about involvement. So unless you mean to tell me that LBJ somehow managed to contact two guys who at that time were loyal to the Eastern Bloc to basically parrot his statements about the Russians being to blame, I think you really need to rework your theory.