If reading up on brainwashing teaches me that certain signs characterize it, and LW demonstrates those signs, I should increase my estimate that LW is brainwashing people, and consequently that I'm being brainwashed.
Reading up on brainwashing can mean reading gwern's essay which concludes that brainwashing doesn't really work. Of course that's exactly what someone who wants to brainwash yourself would tell you, wouldn't it?
Sure. I'm not exactly sure why you'd choose to interpret "read up on brainwashing" in this context as meaning "read what a member of the group you're concerned about being brainwashed by has to say about brainwashing," but I certainly agree that it's a legitimate example, and it has exactly the failure mode you imply.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.