If you are not running Plex Media Server on the Synology NAS, you do not need to give the user Plex (DSM6) or PlexMediaServer (DSM7) any file permissions.
To completely remove Plex Media Server from a Synology NAS, see FAQ 9: Uninstalling PMS - Completely start over.
The username you are using for SMB/NFS mounts on your other system will need at least read only access to your media files.
