This seems to be quite a clear case to me.
Casinos have right to close player's account anytime so I don't have an issue with it. On the other hand, they can't allow you to deposit money and play without giving you a real chance for winning.
First of all, if you submitted correct information about yourself during the registration process, it's casino's fault they didn't cross-check it with any database they use and didn't deny the access immediately.
Secondly, I believe the right approach isn't returning your deposits, but paying out the winnings. If they only returned the deposits, it would mean that you didn't have a real chance for winnings. If you didn't win, but you'd simply lost all your deposits, I assume they also wouldn't contact you proactively, offering your deposits back. If you lost, you wouldn't even know you couldn't even win.
What are going to be your next steps may I ask?
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