You could install Linux on a PC, mount the drive and reset the permissions. THis is messy and could cause numerous other issues.
You could install FFP, enable Telnet, then login and issue a chown/chmod command on the directory. Then remove FFP (or just leave it there).
You could write a small shell script with the chown/chmod commands in it to reset the ownership/permissions, name it "fun_plug" and put it in the appropriate location. A restart of the NAS will run the script automatically.
Unfortunately I've seen other posts on this topic, although it seems fairly rare. There may be other options that work, but these are ones I can think of off the top of my head.
Edit: Another option would be to back up the information, reset the NAS and reformat the drives, then restore the data.