Sort of.

I am making an assumption that there are some people who are likely highly motivated to take action. Parents often care about bullying of their own children, even when the rest of the school doesn't. We wouldn't need all parents to care, just a few of them.
I'm not assuming that lawyers are generally willing to work for free but I do assume that they like money and are willing to take cases on contingency, if they think the case is strong enough.
I'm also going on my understanding that video evidence tends to be fairly strong and that this translates into a higher probability of a favorable judgement with less work on the lawyer's part.

So it's less that I'm making an assumption than that I'm asking where the gap in the above reasoning chain lies.