The head of the CIA, it seems to me, would think long and hard before he admitted that former employees of his had been involved in the murder of the President of the United States-even if they weren't acting on behalf of the Agency when they did it.
In 1975 a Senate committee headed by Frank Church found that the [Central Intelligence] Agency had planned a number of assassination operations, using everything from poison to machine guns and sometimes mob hit men
The CIA could not face up to the American people and admit that its former employees had conspired to assassinate the President; so from the moment Kennedy's heart stopped beating, the Agency attempted to sweep the whole conspiracy under the rug.