Where this gets tricky (and can mess up BSA reporting) is whether the bank is delivering the loan proceeds TO the customer or wiring ON BEHALF OF the loan customer. For loan proceeds, I prefer to see the money deposited into the customers account and then wired out to the third party, rather than wiring directly from loans in process, for example, with the bank as originator. In some cases, the bank may be wiring the proceeds to the customer at another institution. In that case, I view the bank as the originator.
I view the customer as originator if the bank is sending funds at the customer's direction. I like sending that from the customer's account so that there is a clear picture of payments by that customer, should any question ever arise whether for BSA or other reasons.