I actually thought that Airbnb were having their PayPal moment--where PayPal actually realized it was not in the business of payments, but in the business of anti-fraud and risk management. Then I realized this is probably a bizarre one-off case, and the responsibility lies on the renter, not on Airbnb. Although they could supplement renters with insurance, I don't think this is their 'big test'.

What happens next time? Airbnb will either settle with the person quietly (as they've done successfully in the past), or the renter will sue the person who damaged or stole their property. That's all there is to it.