The Backups folder is used by Server itself; maybe it won't allow other access. From my observation, FMS creates folders in there for each scheduled backup it runs. If you are creating a schedule called SafetyNet, FMS will create the folder when needed. If, however, you are making a backup by some other process, try locating your SafetyNet folder inside the Databases folder instead, and see if that changes things.
I'd look at the permissions a little closer using Terminal. Make sure fmserver not only has rw access but can also execute (x). An example from my server for the Backups folder:
drwxrwxr-x 48 fmserver fmsadmin 1632 Aug 14 15:00 Backups
Make sure it is on the same box. Cannot do a network or usb drive.