In a conversation that is supposedly about how people are being mislead by media we're 2 seconds away of Godwin's law again. It's exhausting.
An idiot who shares something untrue that he ought to have known was false is materially different from someone who fabricates something and ultimately directly and by proxy misinforms 10 million people.
The choice isn't between tyranny or absolute freedom. It's about our actions shaping the bones of society. The current framework isn't mere ground truth we must accept we can reshape it if we desire and perhaps we should.
You can’t just squeeze the screw tighter on this.
The idea of “I know better than you, therefore I control what you see and say or else” is the absolute height of arrogance.
First of all, plenty of the people currently spreading lies on the internet are doing so under their own names and have built some celebrity and a career out of it, so I don't know why you think that anonymity contributes to the problem in any real way.
But more importantly, how exactly do you propose to "punish people" who spread lies? With what form of punishment? Is this a formal system of punishment, or some informal system?
If formal: Under what jurisdiction? How does your proposed system determine the truth, and if it can determine the truth how does it determine which lies are malicious enough to be deserving of punishment?
If informal: How does it differ from what we have today, in the form of people arguing with each other and occasionally trying to get each other banned from social media or otherwise made unpublishable or unemployable?