He stayed in the apts, so he owes you for that night plus the cleaning fee, as well as any nights that you cannot rent the place with such a last minute cancellation. Plus a booking fee for your trouble to re rent it.
Actually , he isn't due any refund....many people lie about why they have to move or cancel a reservation. I hate to say that, but after 3 years of condo rentals in Maui, the top lie is that they are coming for a honeymoon. I have never heard of so many engagements being broken last minute before honeymoons. I don't believe there was a wedding and some single men even forget they lied to me about it!
I guess lots of people won't rent to single men?
Anyway, cleaning people do miss things occasionally, or like you said, there are people who will always find SOMETHING wrong, if they are trying to bully you into giving them a refund.
JUST stay STRICT on your policies, don't ENGAGE with the customer beyond your final statement, that the apt is as PICTURED, he left early, that's his right to leave
Its your right to not issue refunds after someone checks in. If he files a resolution claim, you can deny it and then refer it into the airbnb center to deal with it.