Cases like this are so rare, and although the damage is horrific to one person the dollar amount is trivial on the scale Airbnb operates. Seems like a perfect case for a shared risk pool that actually works rather than insurance.
Then they could peg the cost of the insurance fee at a realistic share of your risk, and the theoretical cost of someone trashing the place would be built into the cost of the room.
Insurance fraud is no joke and it takes a hell of a lot of stupidness to attempt it.
Fraud would mean the owner having an accomplice renter who destroyed something, Airbnb compensating the owner, and then being unable to track down the accomplice for redress. That's only a problem if a significant number of renters are able to use Airbnb without Airbnb having any way to track them down.
And if that's the case, they already have a problem.
At that point Airbnb is put in an impossible situation - they either pay for what may be fraud, or they refuse to compensate what may be actual theft.
So as the owner, it's my word against the renter with the cops involved. They're going to figure it out eventually. Maybe I'd be able to float a few grand for a while before it caught up with me, but surely there are easier ways for me to turn false testimony to my advantage than screwing over the web site that's earning me money?
It is, of course, very possible to set up insurance so it has few loopholes - insurance companies do it! My point is simply that it's not trivial, and Airbnb would have to invest significant resources to make it work well - while still potentially failing to gain the goodwill they need (few people actually LIKE insurance companies).
Is there someone here that can set up a Paypal account for this gal? I'd happily donate a few $.