While I'm far from trusting booking I used late cancellation several times in EU. Usually those offers were more expensive, but I was charged late as promised (like a day before reservation date) and if cancelled before it just worked.

Usually I'm more worried that their places usually just get my credit card number in plain text, write it down in a notebook and some frontdesk person simply uses that CC numbers to charge me on my first day there or so, manually entering it into CC terminal.