The point is, people were saying Zoro killed all those people, and it turns out he didn't, genius.
So just because they called him the Magistrate "Murderer", doesn't mean he actually killed the guy.
Propaganda one - Zoro was murdering people at night - Lie
Propaganda two - Zoro MURDERED the Magistrate..... Yeah, I'll believe it if we go threw the rest of the arc and never see the guy again.