There are 4 usergroup permission settings that might apply and have been set incorrectly. They are in the
DownloadsII Permissions section and are the right near the bottom:
- Can Edit Own Files
- Can Edit All Files
- Can Delete Own Files
- Can Delete All Files
Either of the first or third would let a user edit/remove their own files, while the second or fourth would let another user edit/remove another user's files.