Personal opinion:
Unless there is actual, proper negligence (i.e. the guy behind was pissing about, or riding like a cock) then it’s just a case of “shit happens” and suck it up. If I was the one behind and had properly screwed up and caused the crash, I might offer to fix it for you (£130 for a rear mech + my time FOC) but wouldn’t be too happy to pay £250 for full retail + shop labour, which I wouldn’t even do on my own bikes.
My son was flattened by another rider at the weekend and trashed a set of QR skewers. No question as to blame, but I wouldn’t think to go after them for money – it’s just something that happens when riding and I bought and fitted a new set. In fact, I was actually down, money-wise, as I ended up fixing the other boy’s mum’s chain, so needed to buy another 10sp chain link! These things happen and it’s not worth getting riled about.