I was an Airbnb superhost for a few years. I’m not aware of any incentive for hosts to report damages that aren’t legitimate. I’m also not sure why, if this is due to damages, they wouldn’t attempt to charge you versus ban your account.

I’ve always had surprisingly good experiences with Airbnb’s phone customer support. Perhaps try calling them again to ask for clarification. It could just take connecting to a more helpful support rep.

Best of luck!