Yeah it was an op called Mockingbird , look it up , the CIA had direct control of the media , probably still do .

The JFK case would be pretty easy to solve , find out the imposter who spoke broken Russian but good Spanish that called the Russian embassy in late sept to talk to a known Russian assasin , thus laying the set up / blame at the doors of the communists . Find out who controlled that imposter and it begins to unravel . Hoover knew it was an imposter within 24 hour ( per a memo released after jfk act ) he also notified LBJ shortly after, that audio mysteriously disappeared for obvious reasons but luckily a transcript was dug up after the jfk act .

It was actually a brilliant plan as the CIA mole hunters immediately launched a mole hunt to find out who this was ( Russian and Cuban embassy phones were tapped which was probably as big a secret as there was ) which resulted in a ton of paper trail between DC and Mexico City, thus creating the ultimate blackmail that LHO was some type of operative and that telling the truth would destroy our intelligence gathering from the taps on the Mexico City stations . It's not a coincidence the WC totally by passed the odd Mexico City acts .

A lot of people fail to realize the official govt position is that JFK was killed by a probable conspiracy and the DOJ should re open the investigation .

The fact they didn't tells you it was likely some intelligence guys ( likely the rougue group that was supposed to kill Castro ) . Intelligence operators are pretty much above the law .

By now most know who the actual assasin operators were with several anti Castro Cubans as the shooters ( Diaz etc) and their CIA sponsors that were part of the executive action team - in Moralez , Bill Harvey , Rip Roberson , David Atlee Phillips , Ted Shackley , tony sforza and their mafia counterparts rosseli and Martino , heck some of these guys admitted it .
But the real question is how high it went ? Who funded it , LBJ , Hunt , Murtchison etc. ? Those Nixon tapes referencing the whole bay of pigs thing that his top 2 aides said was code for the jfk hit could be interesting as well