It's been a while since I read it but I always sensed it wasn't completely forthcoming since at the height of the Cold War, for there to have been a strong possibility that a sitting president was assassinated on orders from Moscow, possibly via Havana would have been a casus belli.
See my post #43 a little farther down in this thread concerning the shooter's location.
You may or may not know this—but it was LBJ who told Chief Justice Warren that is was necessary to crush any claims of conspiracy for exactly the reason you stated.
Hint: LBJ was lying. He knew it had nothing to do with Communists or Russia or Cuba.
He was scamming Warren.
That’s the argument that LBJ used to induce Earl Warren to lead the investigative effort. He didn’t want to have anything to do with it, but LBJ gave him “the treatment,” for which he was so famous.