Isn’t this kind of begging the question? It’s implicit in your reasoning that the CIA does exactly what I’ve claimed they generally don’t do.
Anyway, the point is that I don’t think you have to dig very deep these days to find plenty of instances of geopolitical power X doing bad things, so I’m not sure why the CIA would bother lying to stir up shit against them when they could tell the truth just as easily, with the same result. This assumes their purpose in releasing any information at all is to influence public opinion, not increase transparency, as the latter would probably mean divulging uncomfortable truths. The former does not—they can release exactly what they want, and no more.
On the other hand, flatly denying you’ve done a bad thing is a form response for governments and corporations (and politicians) at this point, even when it’s risible on its face. If you’re the guy responsible for putting those comms together and you admit wrongdoing, you’re never working in this town again. Simple as that. Deny, deny, deny. Deny everything. (Isn’t that a one-off X-Files title card?)
Has the CIA lied? Absolutely, though I’d guess far more often (orders of magnitude?) by omission than by outright explicit falsehood. The latter goes against the same ass-covering impulse that drives the bullshit denials. My brief comment above is meant to be a general observation on the sorts of public communication games the CIA and similar organizations tend to play, not an absolute truth or bible for living your life.