As much as I disagree with some of them, I recall the folks at the Accidental Tech Podcast spent a good while on this very discussion back when people were migrating from Twitter to Mastodon, and they had some interesting concerns and conclusions.
The answer is yes, in many places the admin hosting the content could be responsible for the content. Where I live I believe they would have to provide user data about who made the post, and if they refuse, they become the responsible party.