You can set different permissions for different devices, you are aware of that right? I can say my DVD drive is readable by gid x, but not the partitions on my hard disk... This is already what Linux distros are doing.
Then the media player can read every DVD you put into your drive as long as its running. So you always have to close the media player before inserting a DVD containing private files.
That probably isn't that important for DVDs, but for other devices (e.g. microphone, webcam) it certainly is.