I had a similar problem with Fitness First, whereby I signed up at the more expensive price on a 6 month deal to see if I liked it. After 3 months I changed to the year deal as I was getting on really well there, then 9 months after that lost my job and cancelled it.
They also asked me to put it in writing which I did, then a few months later rang me up to say I had missed payments. I called my local gym who said I had to go through head office, I spoke to them, who looked into it and I never heard back from them and never had another call about any missed payments.
If you have a copy of the letter with the date on, there can be no issue. I also took the persons name I handed the letter too. Also I expect she would have had to hand her membership card back in with the letter, so again they could look back to see the last time she used the gym.
Hope this helps!!
But as said your probably better off calling head office rather than your local gym as you will probably just be wasting your time going there!
Good luck