I think the way to get around this is to ask the customer up front if he/she is interested in being qualified for a loan product at the same time the account is established. This is a perfect opportunity to cross sell overdraft protection, credit cards- whatever. If the customer says "yes" then the bank has a "request" for credit and can proceed to qualify the customer for both the credit and the deposit product. However, the downside to this is that the bank would have to generate an AAN if the customer did not qualify for the loan product, the deposit product, or both.
Being kind is more important than being important.