The problem is I can't see all the files on the DVD. I've seen this problem before and known that it has something to do with the Joliet File System extension. Luckily there is a quick fix. A quick check of the man page for mount and then mount_cd9660 shows that the -r and -j options to mount_cd9660 allow the mounting of ISO 9660 file systems while ignoring the Rock Ridge and Joliet specific extensions.
/sbin/mount_cd9660 -r -j /dev/disk1 ~/DISK_LABEL
And voila! All the files are there and all the files are mapped to uppercase. No sudo is required with this method.