I agree with you. In that context, (1), (2), and (3) are correct and are saying the same thing, but (4) is incorrect in that context because it is saying something else.
In (1), (2), and (3), the tyrant's being overthrown is presented as a necessary condition of the interlocutors' being free.
Sentence (4) does not refer to a necessary condition. It states that something should happen for a certain reason.