Most at times when a casino request you to provide your personal information during an investigation, it is to confirm if you're using multiple accounts or if you are operating from a country that their system does not support. If you know you're not going against any of these things then you can freely give them the information and wait for their feedback if they'll come up with some shitty excuses as to why they won't reopen the account.
This text of your means that indeed you're operating the casino from an unsupported country, and if they should refuse to open your account they have something to back their action even if you take them to a third-party to judge the case.
And how would they know that? When withdrawing you're providing your wallet address not another casino's name. So I'm curious to know how they'll be able to identify that this is a casino deposit address.