I haven't used Jungle Disk, but I seriously doubt that that is a requirement. I can't imagine a backup server system that doesn't allow backing up things that are on other servers one way or another.
You should also be able to see all your users' files on shared hosting with any FTP program.
Besides a backup on the same system doesn't make too much sense. If you have a problem with that system, your backup is gone too. You need to backup somewhere else. (Maybe Dreamhosts' Dream Objects is something for you?)