The reason non-violent methods work is because they are implying that if you don't pay attention to the non-violent methods, the only recourse left is violence. Because realistically, if your non-violent methods are easily enough ignored, they'll be ignored.

And historically, violence has been an excellent tool for change. Not always for the better, that's for sure, but to deny that mass violence, especially targeted at those deemed to be in power, doesn't change things is ignoring basically all of human history.

Speak softly, but carry a big stick.