If you watch the media coverage the day of the assassination, they did several “man in the street” inteviews to get peoples’ reaction to the assassination. They almost all said they thought Right-Wingers did it, and the interviewers were basically feeding them the lines. So the media was definitely in on “The Right-Wing did it!” meme.
I was in class in Air Force tech school at the time the news of the assassination broke (noonish as I recall). Even the instructor (a captain) blurted out something to the effect it must have been a right wing job because...Dallas. Never forgot..thought he was FOS.