Although there have been negative PR effects for Airbnb due to this incident, it appears that they have benefited as well, by wisely using the lesson learned to improve their business by adding essential insurance and pre-deal inter-member communications services, among other things. The future value of that benefit to a start-up company most likely far exceeds the damages suffered by this host, assuming the PR issue can be positively resolved. There was no similar benefit for the host, unless you count the lesson learned that they should avoid the sort of activity your business is built around.
So here's a suggestion: acknowledge publicly that this incident exposed ways in which the service could be improved and offer to make this one host whole as compensation for that value. Solves everybody's problems in one fell swoop without accepting blame for something that isn't Airbnb's fault (and more importantly without resorting to blaming the victim - not the host's fault either). I'll bet it would cost far less than the usual media blitz companies commonly use to repair their images after incidents such is this. Consider it a good investment in the company's future.
So here's a suggestion: acknowledge publicly that this incident exposed ways in which the service could be improved and offer to make this one host whole as compensation for that value. Solves everybody's problems in one fell swoop without accepting blame for something that isn't Airbnb's fault (and more importantly without resorting to blaming the victim - not the host's fault either). I'll bet it would cost far less than the usual media blitz companies commonly use to repair their images after incidents such is this. Consider it a good investment in the company's future.