I think there is a lot of truth in the following:
From Defrauding America, Rodney Stich, 3rd edition 1998 p. 638-639]:
"The Role of deep-cover CIA officer, Trenton Parker, has been described in earlier pages, and his function in the CIA's counter-intelligence unit, Pegasus. Parker had stated to me earlier that a CIA faction was responsible for the murder of JFK ... During an August 21, 1993, conversation, in response to my questions, Parker said that his Pegasus group had tape recordings of plans to assassinate Kennedy. I asked him, "What group were these tapes identifying?" Parker replied: "Rockefeller, Allen Dulles, JOHNSON of Texas, GEORGE BUSH, and J. Edgar Hoover." I asked, "What was the nature of the conversation on these tapes?"
I don't have the tapes now, because all the tape recordings were turned over to [Congressman] Larry McDonald. But I listened to the tape recordings and there were conversations between Rockefeller, [J. Edgar] Hoover, where [Nelson] Rockefeller asks, "Are we going to have any problems?" And he said, "No, we aren't going to have any problems. I checked with Dulles. If they do their job we'll do our job." There are a whole bunch of tapes, because Hoover didn't realize that his phone has been tapped. Defrauding America, Rodney Stich, p. 638-639]: