I was with Anytime Fitness until I moved, and I could only get out of my contract by sending them a copy of my new driver's license. I was willing to pay the ETF, but they demanded I show them my license in-person to get out, when I was hundreds of miles away. Finally I cancelled the card they were charging, let them sweat for a bit, then called and said "offer me some other way and you will get your money". They then let me email them.
But yeah, if I didn't have proof that I moved, I would have been stuck in the contract forever.
I had a record showing that I had tried to be reasonable, so if anyone reasonable was willing to talk to me, they could see that. But the reason I didn't just cancel the card and leave it at that is exactly that reason. After a month of them trying to bill me on a cancelled card, I called them and offered to pay the ETF PLUS the late fee if they would just let me email them proof that I had moved. It was still cheaper than flying back just to show them my drivers license.
But yeah, if I didn't have proof that I moved, I would have been stuck in the contract forever.