Logic above aside, if the other bank paid out the funds, "the depository bank would possibly realize their customer is a fraudster" is only going to ensure they want the money from your bank sooner rather than later.
I will say that once upon a time, in a bank far far away, a cashier's check was issued that should not have been. A gal at our bank with a strong personality called the bank we knew was getting the check. The customer drove straight over. Our gal told that bank's cashier (who she knew) that we would not honor the check.
It was a bluff, it wasn't legal, but the customer came back to our bank to discuss the matter. (FWIW I was but a peon in the bank at the time, an observer.) That, and the (stupid) loan that funded that check were both taken care of. We were lucky in more ways than one and the new lender did not last long at our bank.
I give you that story not because it worked, but because losses could have been greater had the customer gone to a savvy attorney and not back to our bank.
My opinions are not necessarily my employers.
Rules and Regs minus Relationships equals Resentment and Rebellion. John Maxwell