I like the theme, but the fact that the player must know that the character is wrong is... strange. I think it's difficult to have a player "fight" for the character if they feel like it's useless.
So, how blatantly false must the belief be? Must it be to the point that there's no chance of twist ending? Because I, as a player, would probably still keep the hope that in the end the protagonist turns out to be right.