Hi
If you are not a regular visitor to the bank, they might ask for bank cards, photo driving licence or passport, so that the have some confidence when giving their signature. I have not heard of a bank refusing this before but I guess that most people don't visit their bank regularly, so the banks don't know most of their customers by face.
The bank would have a written procedure to follow when being asked to sign forms to confirm identity. If they could not sign the form, they should have advised you why this way.
The organisation that is seeking the identity confirmation should have a list of people authorised to sign the form. If the bank won't do this, go to one of the other people that can do. Is there someone you work with or for, that can sign the form?
Huckster