Just chiming in--I think Airbnb will support what they tell you, but best to have any communication documented just to aid the process. They have backed me in the past with other issues/bad guests/a dispute.
I had guests that I booked privately damage things and steal really weird stuff from me, like Hershey's syrup (3 bottles) and expensive toothpaste! And maybe a yoga mat, not totally sure about that. And they damaged an expensive electric tea kettle, and took a trash can (they had a party which was allowed).
I bugged the guy for at least a month but he did eventually put $100 in my account, as requested. The other items I noticed later on, I can't REALLY prove it (but who else would come in my house and take these things! No one!) but it bugs me still! The good thing about Airbnb is people do have the threat of a bad review, but often you don't realize something little (but annoying and really uncool) until later. I've had other guests tell me they broke a wine glass, could they replace it, they ruined a rug, could they replace it, etc. Very appropriate ettiquette and I always so no, as they are minor things and cost of doing business AND they did the right thing and said something to me privately.
Finally, I only put a damage deposit on my main/high priced house since I feel it's something that is off-putting to potential renters, and I don't have that much to lose in my more simple rentals. It's something to consider. I keep it simple to attract rentals.