Their part of the proof is simple - they can prove that you signed a contract to receive service. They keep offering this service. It's then up to you to claim that you attempted to resign from this contract. How would you prove this? It is you who are claiming you attempted to close the contract.

The contract as you signed it might well contain a clause that explicitly says you have to perform arcane rituals to stop the subscription: now you have to have the bank analyze the law in your place of residence on whether the contract itself might be illegal. I do not live in the USA and don't have experience with the credit card dispute system, but I personally doubt that this level of legal analysis would be performed by the bank for your, free of charge even.

I have no doubt that you would win this in court, by the way.