” depends on what sort of agreement the agency has with the bank. But the fact that they (agency) has told the buyer that he would have to pay them a commission, I would assume the bank has no standing agreement “
Yes, it does depend as to what kind of Agency agreement they have. I am sure that no Agent will show this to his/her client and you have to take his/her word for it. The bank may have this agreement in place or not , however this will not stop the Agent from increasing his/her income stream from whereever possible.