Android : adb root shows root access but does not give it

I have a Galaxy S4 (GT-I9507) which is rooted with busybox installed and the CWM custom recovery. I recently made a Nandroid backup and since I don't have an sdcard, it was stored in /data/media/clockworkmod/backup/ or /mnt/shell/emulated/clockworkmod/backup/. Now, I can't move this using a root explorer app to an area accessible via USB to back it up to my computer since I don't have enough room left on my phone, so I've been trying to copy it to my PC using adb pull. Thing is, I'm on a stock ROM so my original adbd binary does not allow adb root. So I installed Chainfire's adbd Insecure app and enabled it. Now when I run adb root I'm told that adbd is already running as root. When I do adb shell, I get root@jftdd:/ #. However, adb is not actually running as root. It just appears to run as root. It says it's running as root but if I try ls /data/media/ I get Permission Denied. Until I actually do

adb shell su ls /data/media/

I continue to get Permission errors. This means that adb pull /data/media/clockworkmod/ or adb pull /mnt/shell/emulated/clockworkmod/ fails too because despite adb saying it's running as root and looking like it's running as root it does not actually have root privilege. My question is how on earth do I actually get it to have root privilege so I can pull my CWM backups without permission errors?