As the site had been hacked and they have no backup of that database, I do not think it is possible for them to refund base on the information of deposit from a wallet. Think it yourself what will happen if same claim occurred by multiple person? You may think it is not possible as you are a legit users but there are a lot of people who will try to take a chance for the exploit of the site. I think for now they have no alternative to verify except the email which was on the receipt on the email.