I’ve watched the live coverage many times.
Cronkite just *knew* it was a right-winger, they kept referencing Adlai Stevenson getting attacked in Dallas a few weeks before by “right wingers”.
That’s why I believe there are all the Conspiracy Theories, because they don’t want to admit that a Commie did it.
Like JFK himself, Cronkite was in the chrysalis stage of becoming a full blown Delusional Lying Leftist as we see in full manifestation today.