The action of assessing information? That's not at all authoritarian, unless we just think that the very act of wanting to know the truth and of saying that truth is better than falsity is authoritarian, which we shouldn't (though I get the sense that some people do). If there's an attempt by the gov't to suppress opinions or genuine errors, that would be a problem to those of us who believe in freedom of speech.
I think it's useful to go back to the point I made in the other thread, about Orwell. The liberal idea is that in order to have a society and gov't guided by science (not just natural science), people have to be able to tell the truth (including moral truths) to the best of their ability, and entrenched hierarchies will always be a threat to that (because the process of developing our understanding and advancing is never-ending--as RZ sings, "don't speak too soon for the wheel's still in spin."). As a result of that, we need to elevate support for freedom of speech above support for any existing power or we face the danger of being stuck. We end up incidentally having to protect lies because we don't know what people are thinking (though materially injurious lies--fraud--are sanctioned). But there's no basis in such thought for the idea that calling out lies is bad. They should be called out and disrespected, and people should shun them.
You didn't respond last time, but I think it's clear that there is no similar rightist basis for freedom of speech as a principle (there often is a move by rightists to destigmatize far-right views for practical reasons).