Would you say that oil companies do not impose environmental externalities, but that the guilt solely falls on drivers who consume gasoline? No, the company bears some responsibility.
As to your second question, this is a public policy issue, and there will be a policy response whether AirBNB likes it or not. I think it would be smart for AirBNB to engage in the policy conversation.
If there was a bulletin board that was primarily used for activities not permitted by local law, the board would likely be taken down. For example, if there is a bulletin board in a dorm that is used to advertise different drug delivery services in town, either the board will be taken down or a new requirement would be placed requiring all postings to be preapproved.
Craigslist is an Internet bulletin board that chose to remove a few categories due to pressure from law enforcement and the community.