1) CC statements
2) I don't know about your gym, but my membership card won't let me through the door if it is expired. Most memberships have an expiry date, and I doubt ANY gym gives you the membership based on your word. The fact you have a membership proves you paid.
3) It is their word against yours and they admitted that they had someone stealing membership money
4) change gyms to a less shady one (60$/month is pretty cheap for a Gym Membership)