This situation is in fact a very understandable vendetta of the unfortunate victim towards the rest of the world - and she is right - everyone should pay for what she suffered. The actual word is compassion, and there's never enough of it in the whole world for any single unfortunate person.

With that said, no company with AirBnB's business model can publicly say they will assist victims whatever the cost. It's just impossible. It would be a blatant lie. They must at least maintain some sort of windshield against insurance frauds, and doing that requires tons of hard PR and legal decisions to be made, and the assistance of lawyers. And everyone hates lawyers. Companies are sometimes inherently good, sometimes not, but they should never be inherently so stupid as to sign their own commercial/financial/legal doom. You can get up from bad PR, but you can't get up from bankrupcy.

Now after this argument in favor of an actual public silence, let's see what we have:
1) a victim
2) there is no 2. There is a victim and that's all.

Just fix the victim. No need to go through internet flamewars or PR messes, no need to even listen to that. Airbnb should just send a team of 24/7 dedicated people with quasi carte blanche (within what the company can afford, of course) to see through that victim gets better, if that objective can even be met. If the "get better" project goes so wrong as to lead to law suits or whatnot, then let justice decide, because in the end, yes, someone has to pay for what happened, and the legal system is here to decide who should pay.

Now about PR: switch the debate from a "what did AirBnB do in that situation" witch-hunt to "This is what we are doing, this is how it's going from our point of view, now what do you (Mr/Mrs Customer) think we could improve on?". Open a public discussion on your social network and dedicate someone to analyze public input. And use it the next time something like this happens (because unfortunately, it will happen again). Centralize this debate somewhere where you can handle all this information, and by "handle" I don't mean "censor" but of course "assimilate".

...and just ignore those stupid emergent flame wars between big internet guns who are mostly in for pride (white knights & trolls) and money (journalists, consultants, lobbyists & investors). Let them deal with the crap they fling around themselves, and keep focusing on the "get better" project: the victim asked specifically for your help, and that's what really matters here.

Related link: an analysis of an excellent online PR crisis management by Monoprix (in French only, sorry) http://guybirenbaum.blogitexpress.com/91728/html
The "victim" (an employee who got fired for taking home unsold & trashed goods) explained that he "tried hard to make a fuss and a buzz" of his situation because he felt that nothing short of prosecution and trial could make him feel better. This is a case of a failing "get better" project with exemplary PR - and to be honest, it's only when the project fails that PR become important. What did Monoprix do? They centralized the debate on their Facebook page, switched the focus from "Monoprix is bad" to a laconic "here's what we are doing, tell us what we can improve on" and they have dedicated Community Managers assimilating and discussing the comments instead of censoring them.