So when social media companies add content (such as fact checking), they can now be sued for libel because they now have their own content and are now publishers. They can still censor since they are private companies but can now be sued for libel.
I realize this is an attractive argument but it isn't reality. In fact it ignores the heart of the issue.
We have a law called the Communications Decency Act that specifically addresses this situation. It arose because people were wanting to sue Prodigy for moderating posts on their system.
Congress thought the fear of liability would hinder the growth of the internet so they explicitly gave protection to service providers to moderate content and restrict users.
We may wish that wasn't the case and we may think it isn't fair, but it's the current state of the law.
This is the same law, by the way, that let's Jim delete FR posts and zot users without fear of being sued, so think about what it means if you throw it out.