If the bank is sending checks drawn on the bank's own account, then you are right, those checks will not bear his account number. Those checks will also be paid for up front, rather than at clearing. Oh, and I've never seen a bank offer a service even remotely like that as a mainstream normal activity, while every bank in the country is completely willing to print and mail checks bearing the customer's account numbers, either for free, or for a nominal fee.
I have a client in Austria who pays me this way. He logs into his online banking and directs a bank payment. I receive a payment from his bank's US affiliate, from a special outgoing payments account. (He doesn't have an account in their US affiliate.) The only personally identifiable information of his that it contains, I think, is his name (though I didn't look very closely).
This may be an Austrian thing, something specific with his bank, or something like that. I never really thought about how unusual it was.
