Sorry for the late reply... but "tis the season".
Okay, most would say since the user has full access there... there should be no problem.
I might suggest making system (root) the owner and admin the group, and giving others
basic read/search access:
sudo vsdbutil -a /Volumes/Media
sudo chmod 1775 /Volumes/Media
sudo chown 0:80 /Volumes/Media
That should work. (1st command redundant, but no matter).
P.S. - Don't rely on "permissions" to secure an entire volume.
Even though you locked yourself out, any admin could get in.