Related to the previous post, and deniability.
Of course a fist in your symbol implies violence. Why else would you use it, except to show that someone is willing to use violence? This is not to say that everyone who uses that symbol intends on doing violence. People generally don't think that clearly and trace things back. It likely is more of a feeling, a feeling of "We are serious and we are angry!" Yes, serious. Yes angry. And a fist symbolises this...why?
It may not be conscious, but it's not an accident.