I don't think I've ever seen any form of "censorship" of the type these guys complain about. There are tons of threads that describe problems and issues with CGC that have been allowed to stay on the first page of CG for months at a time, even with the participants doing little more than repeat themselves ad nauseum.
The deleted posts and locked threads are almost always related to rules being broken - common sense rules relating to threats, instigation, profanity, nudity, murder memes, hate speech, etc.