"..but who issues/hands out the passwords?"
An organisation in which I worked had this system. The passwords were under the control of a Security Manager. He had no role as a systems or network administrator - his role was solely to control and monitor access and changes to operational systems.
To the person who suggested many people would have backdoor access: not likely. Regular audits would uncover this and anyone found to be accessing systems in this way would be subject to instant dismissal and possibly, legal action.