Actually, they can and will be held liable
That is a matter for a Court, anybody can sue or threaten to sue anybody especially of course in the US. I would have thought you would be more focussed on the personal injury aspect than the door. That tends to be a much much larger sum.
Due Dilligence
This would be certainly an interesting legal development if a person renting a room and their booking service was required to undertake such a detailed background check. Simply does not apply, would kill the Hotel/Accomodation business stone dead. And quite a few other businesses. Can not imagine Home Depot would be renting too many chainsaws....
Damage to other people's property
They provide the Host with limited Public Liability Insurance, you can read about it on the AirBnB site, can not see how it applies in this case. Of course all Hosts should have a comprehensive Insurance Policy of their own, but yet again for your situation there has to be a basis to hold the Host liable.
I am a really small Hotel, but yes it a Commercial property and I have to comply with all fire regulations etc. My property was built as a Hotel, it is is a historic building I am still working on restoring and will be at max a 8 room Bed and Breakfast. With 3 rooms AirBnB suits my current operation and style and I will no doubt continue using it in part. I personally know a local 20 room Hotel that is listed on AirBnB, largest I have seen pinging around had 100 ish rooms, usually larger operations list a few of their rooms to get exposure to the AirBnB booking system. Obviously having all your eggs in one basket and just using one booking system is risky, I assume the larger operations use mutiple booking systems and their own direct site. I used to have my own web site but with just 3 relatively cheap rooms not currently worth it.
There is a whole range of properties on AirBnB, I think the minimum is $12 a night, in some areas there are properties listed at many thousands a night, everything from a sofa to muti million dollar properties. Yachts, tree houses, Camper Vans, you name it.
AirBnB has a bit of gloss to try and differentiate itself but at its heart is a booking system, the Trust aspect is just gloss.
Anyway I am intrigued to see how things go, please do keep us updated.
David