Here is a quote from Airbnb Help, @Abby38: "Offline or cash payments are a violation of our Terms of Service, and can result in removal from Airbnb."
That comes up when you type "cash" into the Help search bar.
A host can charge for certain extras through the resolution centre, I understand, but not if it is not stated upfront on the listing page.
A good host will not surprise you with any cash requests. If a bad host does, just say no. If they insist, give Airbnb a call.
Just curious - someone charged a cash fee to use the bed? Where in the world was that?