Don't lay all this at the doorstep of the Russians, leaving them clothed in the appearance of the Dark Side Evil Empire.
It started with Goebbels, Harold Laswell, and some others in the early half of the 20th century. After the defeat of the Reich, CIA "rescued" sociologists, psychologists and others who had worked under Goebbels, just as they picked up von Braun for the NASA programs.
They spent about $1 billion per year for 16 years between 1945 and 1960 to develop and refine psy-war and propaganda practice. The JFK assassination was the blow-back of some of this, but not the conspiracy-a-go-go involving the upper echelon of the agency.
The Russians didn't have the social laboratory to conduct the experiments that the American academics working for CIA had available. No pluralistic media; a total autocracy in which citizens would know the origins of everything that appeared in the news.
After the end of the Cold War, the Russians may have figured out the underlying connection between the movie "Manchurian Candidate" and the assassination of the president a year after the film release. They may have misinterpreted it, thinking that it was "conspiracy-a-go-go" and a CIA monster-plot.
Now -- they've caught up -- the Russians have caught up. Congress put the kibosh on the CIA initiatives in the mid-70s as a result of the Senate Intelligence (Church) Committee hearings. Things you see in the media today, like the Bourne Trilogy, Legacy and "Jason Bourne", are the myth derived from all the factual threads. I would suspect that some folks see the Bourne movies and develop a set of assumptions about today's CIA. That's probably a source of the paranoia and "Deep State" fantasies of the Alt Right.