If customers can no longer trust you to treat them with even the lowest degree of respect (and bodily integrity, already a sore point with air travelers is undeniably a part of that) then you're in trouble.
Witness the stock markets response today, no amount of legal wrangling will make that kind of beating right, besides the obvious ethical angles.
UA failed, then failed again during their initial apology and now may be able to put this behind them but it will be a very costly lesson.