They couldn't admit that JFK was killed by one of their own -- a leftist named Lee Harvey Oswald who didn't like how JFK was treating Castro, and not some right-winger for domestic policy reasons like civil rights.
The liberals did not want the focus on Oswald and his left-wing sympathies, so they shifted the blame to some kind of right-wing something in the air.
The very day after JFK's death, the NY Times ran two articles on the front page -- one, a straightforward news article about the shooting and the accused shooter and his background. The other article was an opinion piece by Scotty Reston with the slant that some element in the country (i.e., mean conservatives) was really to blame. So the myth-making started early.
It was not about who really pulled the trigger, but about shifting the blame for political reasons.
I wanted to verify, it's been 15 or so years since I recall Grant telling the story on his radio show out of WOR. Yes the liberal nut cases blamed Pyne and the emerging modern conservative movement.. the liberals even tried to connect Barry Goldwater to the assassination. We Goldwater supporters were branded "purveyors of hate" even by the Republican likes of Mitt Romney's father George.
I noticed on the same youtube page is a recording of when Grant filled in for Savage. Grant was so popular that IIRC Savage contacted the station that he'd do the remainder of the show and Grant could leave. Grant had some things to say about Savage later.
I know—I heard the same points discussed by Rush and others around the time of the 50 year mark of the assassination in Nov. It made a lot of sense and I should have figured it out myself.