What about the definition of "established customer" in the BSA?
(p) Established customer. A person with an account with the financial institution, including a loan account or deposit or other asset account, or a person with respect to which the financial institution has obtained and maintains on file the person's name and address, as well as taxpayer identification number (e.g., social security or employer identification number) or, if none, alien identification number or passport number and country of issuance, and to which the financial institution provides financial services relying on that information.
or the actual CIP citation...
(2) Identity verification procedures. The CIP must include risk-based procedures for verifying the identity of each customer to the extent reasonable and practicable. The procedures must enable the bank to form a reasonable belief that it knows the true identity of each customer. These procedures must be based on the bank's assessment of the relevant risks, including those presented by the various types of accounts maintained by the bank, the various methods of opening accounts provided by the bank, the various types of identifying information available, and the bank's size, location, and customer base. At a minimum, these procedures must contain the elements described in this paragraph (a)(2).
I'd have a hard time arguing you don't know the true identity of your customer, even if I could somehow successfully argue they don't meet the definition of an established customer.