There is already a mechanism for conveying liability to the publisher (not the platform, but the tweeter/poster, as it should be) when they publish false claims of fact (ie lies).
I see many reasons why, the first of which is just that most of the time the damage is already done by the time it goes to court, assuming you can find the real name behind the usernames that professed lies, and I'm not even talking about bots.
That's why the liability has to rest on platforms -- and that's in addition to the publisher's liability.
Edit: formatting