How much one decides to believe a particular statement from organizations that claim never to be able to provide proof is entirely dependent on one's need for that statement to be true. If that statement provides for the destruction of "the other side" people are much more likely to believe it.

>everything the CIA says or asserts is now somehow in question

The CIA is an agency where everyone is taught to lie. They of course call it something else, tradcecraft, but they are, by profession, liars. A good spy knows to trust no one, especially not other spies.