Ask HN: How to handle cc disputes when customer fraudulently backdates request?

I was surprised to see that my startup recently lost a credit card dispute even though we submitted proof that the customer requested the cancelation after the renewal had already gone through. When I looked into the dispute history, I was able to see that he claimed to have requested cancelation several days before the renewal, when in fact his request came several days after renewal.

The true date of the request was evident in the email screenshot I submitted in my reply, so I'm not sure what else I could have done here. It wasn't a huge transaction, but I'm concerned to learn that if customers lie about when they requested cancelation, there appears to be nothing a merchant can do to win the dispute.

Does anyone have any advice?