It's not about proving something, it's just a certain attitude towards handling these kind of things.
Ever since I was a kid in school I never tolerated people getting bullied. Just because you don't perceivably react doesn't mean that there's no conflict. The conflict exists from the second that they'll manage to bother you. That might take a while depending on character and it might take even much more to actively react. But then I see nothing morally wrong in taking adequate measures to even out the situation.
If simply ignoring them gets you there then that's cool. But as a matter of fact, most people are not that cool, it will aggravate them at some point and then ignoring them still might get the bullies pissed but you'll leave the situation being pissed yourself? Why let that happen when there are sensible things you can do, that'll get you instant satisfaction?
To put things into perspective: In the scenario described by John, I would have simply scared these dudes (IF they would have managed to bother me and that's not that easy), without taking hand at them or their assets. I have that presence. And the look on their faces will probably leave me in better spirits than just sucking things up.
@ Lord Foul: Exactly. Good question.