Don’t forget Lee Harvey Oswald.
The FBI and CIA had very thick files on the guy—he probably was sent to Russia as a CIA undercover agent.
His case officer at the CIA was James Jesus Angleton—chief of counter-intelligence who specialized in intricate plots.
Maybe there is a new Angleton in some dark corner of DC.
Here are the declassified documents:
Hoover: while he's over there something else is going on as well, June 1960