This isn't really a conspiracy, this is the "cognitive infiltration" technique advocated by Cass Sunstein. Basically, even if the government doesn't like conspiracy theories (especially ones around purported government action/inaction like 9/11 truthers, JFK assassination, etc) they can't ban it or punish people due to the First Amendment. Therefore the best approach for discrediting them is infiltrating the movements and pushing them to even more bizarre extremes, so that "normies" will not become interested in what they're peddling.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1084585