Least privilege—the idea that each person in your organization should have the least number of privileges they need in order to accomplish a given task—is an important security concept that needs to be implemented in your backup system.
The challenge here is that network, system, and backup admins all wield an incredible amount of power. If one of them makes a mistake, or worse, intentionally tries to do the company harm, limiting the amount of power they have reduces the amount of damage they can inflict.
For example, you might give one network administrator the ability to monitor networks, and another one the ability to create and/or reconfigure networks. Security admins might be responsible for creating and maintaining network-administration users without getting any of those privileges themselves.