There are a few of incorrect items in your post.
1. This was not a case of a receipt not printing or being damaged or unreadable. They had not 1 but 2 copies of the folio.
2. For this shop you had to book directly with the hotel. Not hotels.com.
3. This had nothing to do with a hold. Holds don't show up on receipts. Normally hotels put a hold on your card when you check in for the total plus $x per day of incidentals. When you check out they clear that hold and charge your card for the total amount. This is the amount that shows up on your receipt. Which I had. 2 of.
4. This is the client's hotel. They should know their own cancellation policies. This shop was not for the chain. Like in a fast food shop let's say it was a McDonald's location but the shop was done by the owner of the restaurant not McDonald's themselves.
5. The instructions did not say cancel the second night at check in. I don't have the guidelines in front of me but the instructions said to cancel the second night somewhere between 10pm the night of check in and 12 noon the following day.
What you are suggesting is when you do a Five Guys shop and they charge you for a cheeseburger instead of little cheeseburger so when you turn in your receipt they say oh they should have only charged you for a little burger, I know your receipt says a regular cheeseburger but we're gonna need your bank statement to make sure you were charged for a regular cheeseburger and not a little cheeseburger.
There are reasons that a body stays in motion
At the moment only demons come to mind