Conspiracy theorists, unlike normal people, find it easy to believe that people will expend enormous effort to create an illusion. I'd like to take this opportunity to say we told you so.
The question isn't "does it happen", the question is "how common is it?". If a normal person is dealing someone who seems to have an "everything is always a conspiracy" worldview - then "that stuff doesn't happen" can be both an assertion that the non-normal is nuts, and that the very frustrated normal just wants them to shut up and go away.
As a prior, I'd assume that the conspiracist is probably more willing to "make that stuff happen". Sometimes, the accusation is the confession.
I'd argue that it's the anti-conspiracy theories, that are just as common and almost as insidious. For example, the idea that the intelligence agencies aren't aware of what their government representatives are doing in the background, and can't/don't influence it. There are literally thousands of individuals who work in the same town with the same people with, their very jobs are to discover and keep secrets, and they are almost all presumably capable. Means, motive, and opportunity. And yet, supposedly of the many thousands, none of them has ever done it without express permission from a judge. It would take a massive conspiracy of group think for it not to happen.
