What's your opinion about Oswald being CIA? I think he was - and that's enough to make me wonder about a lot of this stuff.
My opinion is that between 1959 and 1963 Oswald was at various times in contact with and/or an object of interest for various American, Soviet, Cuban, and possibly other inteligence agencies, which makes it difficult to determine the precise nature of his relationship to the CIA. In October 1960 Otto Otepka, the head of the State Department’s Office of Security, began investigating Oswald in an attempt to determine whether he was a genuine defector to the Soviet Union or a double-agent working for US intelligence. Otepka was unable to determine an answer to this question before he was harrassed out of office by Kennedy's incoming Secretary of State Dean Rusk. Rusk subsequently interfered with the CIA's planning for the Bay of Pigs operation in a way that caused the operation to fail, then the Kennedy administration used this failure as a pretext to replace CIA Director Allen Dulles. There are a lot of variables involved in answering the question of Oswald's relation to the CIA, IMO.