Freedom to sue the perpetrators of false information is also paramount as a check on the press
I am not convinced of the truth of your statement. False information is not the problem. Lying can be overcome by allowing others to tell the truth. ...
So how has this worked in today's world? Badly -- some people aren't interested in the truth, ignore it when told, and preferring "feel good" fake news. Example: Faith.
Apparently Canada has a law against false news, and as a result there is no Faux Noise Nutwerk there.
It is easier to overcome lies when they are not given a grandstand to shout from.
Enjoy