Users aren't nearly as stupid as most technical people think they are. What they are is ignorant, which is not the same thing. The solution to this problem is

Users aren't nearly as stupid as most technical people think they are. What they are is ignorant, which is not the same thing. The solution to this problem is to have a very clear indicator on each channel that it's public or private. If you really want to, make it a link that explains what that means. And you're done. This is a problem in the same way that copy/paste is a problem. There are well-known solutions, it's just modern software that went to crap, not the users.