It would seem that root, by adding one to the disk group, allows those group members to run grub in his stead.
Other commands also may be affected .... fdisk and such, maybe.
I had been trying to figure out how to give a normal user complete control of a removable media device .... on the basis that if a user can insert it physically then user ownership of the device could be assumed ...... while at the same time preventing a normal user from having similar control over fixed devices.
Essentially I wanted a user to be able to use fdisk completely on a USB disk, while preventing that user from using fdisk on a fixed drive. Similar to apply to other commands.
There did not appear to be sufficient separation of fixed and removable drives and the permissions applied to the various commands to allow it.
Seemed to be some legacy schemes preventing what I wanted to achieve.
In its simplest form I wanted a user to be able to completely wipe a USB flash drive, using any and all commands which might require root privilegs on a fixed disk, and use other commands to rebuild the flash disk.
I got totally confused with the number of groups that seemed to be in play .....
It would be extremely helpful to see a table of each of the groups displaying the powers bestowed on their members. Those powers apparently change with distro ... and maybe for other reasons too ..
Adding another group to the list would, IMO, only complicate things even more ...... but I suppose it would get the desired result as outlined above.
Sorry for taking this OT ..... it is a subject that needs its own thread methinks .....