The rep says they handle the support for the new owners, so it would depend on WHY you closed the other accounts. If they have you down as "problem gambler", this would mean any new account opened would be blocked straight away, as it should be. The connection is that they do the support, so have the data to hand, and it would be irresponsible not to protect a problem gambler if they had the means.
However, if this was not the reason for closing the account, they have probably been too "trigger happy" by putting it down to you being a problem gambler, even though you didn't indicate this when you asked for accounts to be closed.
This seems to be a common issue in the industry, where players who close accounts for other reasons sometimes find they end up flagged as "problem gambler", often on a software wide shared database. It seems best to uninstall and allow an account to go dormant, then the casino KNOWS it is down to you becoming dissatisfied with the service. I have loads of dormant accounts, but the only closed ones are casinos that have themselves closed, and possibly Crystal Palace after I told Mr Curran where he could shove his casino