Also, a lot of private chats aren't really as private as you think they are. Most IM services are probably semi-safe, because the sheer volume of stuff coming through there would make it difficult to track and report, meaning that for those they do indeed have to resort to "To Catch A Predator" style stings.
But things like mu*s, IRC networks, all that? You have no real guarantee of privacy. Mu* environments are probably the worst for that, as really the people with permissions (wizards, ops, whatever that particular place may call them) are basically just on the honor system not to spy on you through any number of methods, and of course anyone with server/root/whatever access can see all the information being passed through the mu* shell. Similarly, everything you send on an IRC network has to pass through the server, so those with access to it can just look and see what people are IMing to each other.
Privacy on the net is a tricky thing, so as usual the best thing to do if you're really worried about something you sent on the internet getting out is to not friggin' send it.