@Grace0, David is correct that unwittingly, you left yourself open.
If the guest had cancelled through the Airbnb website, there would have been evidence the the case manager could easily see that he cancelled. It is too bad the case manager did not look at the email (I am assuming the guest sent an email through the Airbnb website) but they do not. Next time, always have guests cancel through the website. My thing is have everything official and through the website so there will never be any dispute.
Also, I suggest you have a limit to the check-out time: say 2 p.m. to 9 p.m. (or whenever your staff leaves).
Chalk this one up to a learning experience. Believe me, I have had many of them.
All the best, Jessica