As retold by Adam Curtis in the excellent BBC three-parter "The Power of Nightmares":
3a. CIA people told new director, "er, boss, that was actually us".
3b. CIA director does not believe his own people.
And of course the whole "Team B" episode (Rumsfeld etc.), where the complete lack of evidence that the Soviets had <weapon-of-choice> was reinterpreted to mean they MUST OBVIOUSLY HAVE <even-worse-than-weapon-of-choice-even-if-physically-impossible> and perfect secrecy, otherwise how could we not have found any evidence?