in-just I'm not too familiar with European laws so I'm not going to comment on those, but here in America we have the Communications Decency Act (CDA) of 1996. The important part is in Section 230 which states "No provider or user of an interactive computer service shall be treated as the publisher or speaker of any information provided by another information content provider"
In other words, online intermediaries that host or republish speech are protected against a range of laws that might otherwise be used to hold them legally responsible for what others say and do. The protected intermediaries include not only regular ISPs, but also a range of "interactive computer service providers," including basically any online service that publishes third-party content.
If it weren't for this law, Twitter/Facebook/YouTube could be charged for the occasional terrorist video or other illegal act that is uploaded to the site.
The only way you could get in trouble because of said content is if you 1) were aware of it and 2) failed to take it down. If you were never aware of it (if it was encrypted or you were otherwise unable to see it) you can't be held liable.
This is another reason I'm making my new private messaging ext encrypted. It prevents forum admins from being held responsible for messages sent between users.