Re: "They also can lose exemption if they monitor content."
Not 'even one comment', but yes -- that's a good thumbnail characterization of how it works in the USA. It's an extension of an age-old principle that the *distributor* of a printed work has scant liability for its content.
The idea is that distributors perform limited review of the materials (content) being provided. No reasonable person would expect his local librarians to read (or edit) every page of every book & magazine, for example.
However, publishers are a different matter. Since they often employ editors and they deal directly with the authors, they are assumed to have greater opportunity for review of all content. This carries implied liability.
Establishing 'Net analogues was tricky. What is 'distribution' or 'publishing', online? After some legal wrangling, we got Section 230 of 1996's Telecommunications Act; it grants distributor immunity to 3rd-party content hosts.
Thus, if a site-owner elects to restrict or edit his user's content, he risks losing his 'distributor' status ('How could I know? I just host the stuff. I can't read/watch all of it!') and could face a different standard for liability.
Again, this is the US view. But in the jurisprudence biz, once somebody arrives at a reasonable-sounding precedent like this, you won't have to wait long before it has an impact on case law, pretty much everywhere.