There isn't a built-in pass-through type of rule, but there are a couple of existing options that should work.

You could create a new check that matches those non-backup emails from the NAS and is set to "Unscheduled" with a default status of Failure. That way any email that comes in to that check will send out a notification.

The other option would be to expand the criteria for your existing check so that it also matches the non-backup notifications. If that check has a default of Failure, and your Success rules only match the backup notifications, then you'll get a failure notification when the non-backup ones come in.

Hopefully that helps, if not, please let me know!

@rrnworks: I know we already chatted about this over email, but I'm going to post here in case anyone else comes across this thread as well

What I usually do in these cases is set the default status to failure, and don't set anything for the success criteria. That way any email that comes in triggers the failure status. Then you can manually review the alert, and force the status back to success when it's been resolved.