[Publius]

Allan Dulles “retired” after the Bay of Pigs fiasco. John McCone was Director of Central Intelligence at the time of the assassination.

[rx]

You're technically right with that, of course, but those folks didn't believe very much really changed just because a 44-year old upstart tells the 68-year old "living legend", "Hand in you're resignation or you'll be fired.". Dulles festered--to put it lightly--over whose responsibility he considered the failure of the Bay of Pigs to be.

Coming up through the ranks of the Office of Strategic Services (OSS, often considered the precursor to the CIA) and serving as its Berlin Station chief, Dulles was the first civilian to run what became the CIA. With such a background, Dulles and his immediate staff retained a great deal of influence that was still paramount for the assassination, just as it was with other activities he oversaw, MK-ULTRA and the Lockheed U-2, for example.

As LBJ knew all that (that is to say, he was probably directed), Johnson saw to Dulles' "participation" on the Warren Commission.