It's a state law question; my guess is that the child is not a "party" to the account and they have not agreed to anything. So, any automatic transfer of the property at death could be/should be challenged by the personal representative. (There would not have to be any animus involved, it's the personal representative's job to make certain things are done correctly.)
If your state acknowledges POD or ITF designations, that would have been the right way to do this.
As this is a "highly valued" customer your best approach would be to say you did some research in an effort to make certain this would work. It will be incredibly tempting to point out that the lender is an idiot, but it may not put you in the best light.
It has always fascinated me that some people are willing to wade into stuff they know absolutely nothing about...