The Oatmeal's content is owned by the creator and is made freely available. FunnyJunk did not even credit Inman, they were effectively stealing his copyright, not merely pirating content.
"Most other copyright holders" -- this is much too general a claim.
Do people really complain if a south park episode is taken down from youtube? No, they don't. South Park episodes can easily be viewed at South Park studios.
Do people really complain that their bootlegged copy of Avengers got taken down from a filesharing site? Yes, but not from a vigilante-style moral high ground. What people really complain about is when invasive DRM-schemes are deployed that prevent normal people from, say, making a single copy of a movie they paid for.
Do people complain when a short youtube clip is taken down (eg, a highlight from a sports game)? Yes. Why? When the clip is not available anyhwere else and it kills the conversation. People linked that video in articles and forums and emails and discussions and now it's gone.
Do people complain when mashups involving copyrighted content are taken down? Yes, because mashups are believed to be fair use.
Do people complain when a home video gets taken down because for several seconds you can hear a copyrighted movie playing in the background? Yes, because that's just fucking ridiculous and I'm sure you agree.
I think you can now see some distinctions between what internet vigilantes tend to complain about and what actually happened with TheOatmeal, and the contradction only appears because you've abstracted and stereotyped way too much.