The effectiveness of silencing someone really depends on how common such silencing is for a given regime. For example, if a regime silences all critics (regardless of whether they tell the truth or lie) an individual act of censorship doesn't carry any information about whether the censored info was true or false.

On the other hand, tons of claims are made against the US government every day, and no action is taken against almost all of them. If the government suddenly acted to silence one conspiracy theorist, far more attention would be paid to his claims, and the action would likely backfire.