This is very sad and unacceptable
IT happend with me also once, that I registered to Chili, where i wanted to play for their Deep Stack Open satelite, but didnt made it at the end at all, just regged there but no deposit, didnt played a hand at all. Than a year passed, i want to log in again to play the satelite, it says my account is blocked. Mail to the support, they frame me up, that i have several accounts with what i cheating, because i abuse their casino bonus with it. I was like WTF
didnt even knew they have casinos. Than after some thinking and mailing with them, it turns out, they based this infromation on the IP adress. (Which could not have been the same when i registered, and when i tried to log in again) This made me think, and it turned out, that actually i was at my work place at the time of registration (this was my IP adress) and someone, who also worked there (usign onviously the same ip adress) really cheated at Chili with the caisino bonus.
What i wanted to tell with this example, and maybe can come handy in your case also, that ask them always to check what kind of IP adress the blackjack player used, or why they think it was you. They know basiclly every information about the user, even what kind of Windows version one uses, so it should not be a big problem for them to find it out.