Oswald screwed up the narrative, you see, right after the assasination, Cronkite and company just *knew* it had to be a Right-Winger that killed Kennedy. And so when it came out that it was a Commie, all the conspiracy BS started.
JFK's widow lamented in her authorized book (now suppressed) over why JFK was killed by a communist rather than to have died honorably at the hands of a right winger.