Seriously? So it's ok if BD punishes someone mistakenly because if they do clearly that's what G-d wants?
According to that logic, we don't have to learn torah at all
1. If they do their full hishtadlus in trying to ascertain whether or not someone deserves punishment, then yes, they are not at fault. We can only control our hishtadlus, the results are not in our hands. There are sources for this but I don't remember what they are at this hour. I keep thinking of Chovos Halevavos, though, so maybe that's it.
2. Why on earth would you say that?