Thats a bizarre ask from the bank officials. Did you ask them to try it in their system first. Because if they try, they can definitely open it without any company code or anything of that sort.
Visited bank to apply for this account today. The bank official first said they would require some company code but later said lets apply in the system first then see. After applying in their system it was allowing this variant. Asked for salary statement and id proofs and it got created...