If the CIA did do anything, it would, by definition be a conspiracy, and therefore could not be believed.
So anything the CIA do can't ever be believed, even if true.
A conspiracy is not the same as a conspiracy theory. Conspiracies exist; a defining feature of conspiracy theories is that they do not refer to actual conspiracies, but are rather false beliefs that a conspiracy exists, where in fact one does not.
It is a confusing name, but we are stuck with it. English is full of such things. This one relies on the most casual definition for the word 'theory' to mean a mere guess (that a conspiracy might exist).
If a conspiracy theorist were to show that his theory was well founded, it would simply become an instance of a conspiracy, and would no longer be a 'conspiracy theory'.