This was an exact point I raised when they attempted to charge an expired card twice and then sent my bill to collections. The gym staff admitted to remembering that I attempted to cancel because I was moving to a place with no Anytime Fitness locations; they refused to let me cancel my contract early without me showing them my new lease, which I didn't have yet and wouldn't have until after I had already left my old city. They also surely had electronic records confirming that I had not set foot in an Anytime Fitness since that time - or else, no ability to prove that I had set foot in one since that time.
That they had the nerve to not only keep charging my card but send the progeny of their multiple degrees of utter failure to collections is exactly why they never got a dime out of me. If anything they owed me money, not the other way around. That hundred or so dollars has since rolled off my credit report, but until then I wore that delinquency as a badge of honor. That shithole of a company can shove it.
...anyway, that'd be the way to enforce it: by checking access logs to see if the customer actually used the service. Don't have access logs? Well then, you know the saying: customer's always right.