The probably with 2 is you then need someone to be the arbiter of truth, and the truth is often a hard thing to find. This would end up letting governments jail people they disagree with. How would you write the law to to prevent that?

The whole point of a court is to find truth. They do it all the time. Actually you would need to prove someone knew something is untrue, because it's innocent until proven guilty. You wouldn't have to prove what you said is true to get let off, just bring enough doubt to ward off your opponent's accusation of untruth.