If /dev/hdb is your DVD drive then it should get the ownership of
root:cdrom, not root:disk. This an identification/enumeration problem
and the proper fix would be to figure out a udev rule or whatever that
would identify it and give it the correct ownership.
Failing that the next best thing would be to create a script that runs
at boot the change the ownership.
I'm not that familiar with either of these things, but just to test the
theory try chowning the device ('chown :cdrom /dev/hdb' or 'chown
root:cdrom /dev/hdb') then playing a DVD.