Oswald didn't do it, and the CIA didn't do it.
The CIA only lied because they were trying to to cover up their link with the Mafia.
J Edgar knew about this because he was wiretapping the Mafia.
CIA higher-ups knew about the rogue Cubans in the Miami station who were moonlighting for the Mafia in their time off. It is these elements who ran Oswald and pretended their actions were official.
We know most of their names. We don't know exactly who did what in many cases, but we have the general landscape. And we have lots of bits and pieces of the specifics.
The tall Cuban who met Oswald at Silvia Odio's house was Bernardo de Torres. The man who drove Rose Cheramie from Miami was Sergio Arcacha Smith.
Oswald is not the one who bought the beers at the liquor store the morning of the assassination. Oswald didn't drink. Couldn't. Alcohol made him sick, he had an allergy.
Oswald also didn't drive. This single fact is an important part of the story, it proves that the setup started almost a full year before Kennedy's assassination. It was a careful, deliberate, and meticulous setup.
The only people with the knowledge and means to do this were the Mafia. The CIA didn't do business this way, but the Mafia was able to leverage CIA resources through their Cuban connections. They had resources in the CIA, resources in the FBI, resources in both Dallas and New Orleans, and resources in private industry including Hughes Helicopter, which is where Radio Man got his radio.
The CE-399 bullet didn't fall out of Connally's leg, it was planted in the hospital by Jack Ruby. That bullet wasn't fired from Oswald's rifle, it was a fake, a meticulously crafted work of art traced to Oswald through its striations.
The Warren Commission wanted us to believe that the bullet passed through Kennedy, exploded his head, then ricocheted off Connally's rib and finally embedded itself in his leg. Yet the bullet was pristine, there weren't even any bits of blood and bone on it and it wasn't deformed in any way. Whereas Connally's leg had shrapnel in it till the day he died.
We already know all this. I'm dubious what a new investigation will tell us that we don't already know. Maybe some particulars (like who the Oswald double was, although it really doesn't matter at this point).
What seems likely is that the Mafia traded their Cuban ambitions for part interest in the Golden Triangle. That's really the sordid part of the story, perhaps of greater significance than the assassination itself. It's one of the big pieces our government doesn't want us to know. And that DOES have to do with the CIA, especially its funding - which has exceeded its official budget every year since before Kennedy.
