Mr Patrick RN, allow me to enlighten you on why this policy is in place and unlikely to change.
The basics: Most people wrong-headedly believe that the VA, as a whole, exists to aid and support veterans in disbursing their benefits to them and caring for them, etc, etc.
The grand irony is that this organization exists to do the opposite. They exist due to the political expediency that benefits must be disbursed, but there needs to be an official gate-keeper for this endeavor.
Which leads to the reason for this policy regarding veteran's preferance. They simply don't want the foxes guarding the henhouse. They want the foxes lined up with hat-in-hand outside the henhouse, and if they give them a few eggs at a time, many will just give up and go away. It saves Uncle Sam money in the red-headed stepchild department of our armed forces, freeing up funding for big shiny useless weapons programs.
Basically, veterans might be too sympathetic and helpful to their brothers-in-arms, making them a poor choice in general for VA work. They weasel around this principle with the policy you listed above, and in nursing its much less impacted than their other departments, such as GI Bill benefit disbursement (good luck finding a vet there) or home loan approval, for example.
The VA is ugly business in general, and makes necessary to this day veteran's advocacy groups such as the VFW and Legion. If the VA did not actually have this mission to deny benefits at every opportunity, including hiring preferance, these clubs would have no need to exist.
Good luck on your mission, god speed.