Ah. Sounds like there’s your answer. He’s a scumbag scammer who just got a free stay from you. Sorry, but these lowlifes are out there trying to game the system. We had someone (many years ago) get …almost an an entire week for free (5.5 days)…because she bitched to Airbnb about our “awful” place, sent in bogus pictures, etc. etc. yes, they gave her back 100% of her money and we were screwed for the remaining days she was supposed to stay with us. Horrible!!
The best thing you can do is send all pics of the locks and state clearly that you want it notated that the guest is a liar and a scam artist trying to get one over on Airbnb and also flag and block them.
Unfortunately, there are scammers out there and Airbnb is fully aware of this problem, but a an outsourced CS rep can’t be expected to know what happened. They probably are just sending out rote messages anyway.
If they do delist you, take the social media route and DO NOT STOP until you speak to someone in charge.