As long as the remote NAS or other partition cannot be mounted programmatically (ie, without manual intervention).

In cases like yours, I would think it much more secure if you had to turn on the power any time you wanted to access the non-local or non-current storage.

This is what is so powerful about tape storage: It isn't accessible to hackers if it isn't mounted. You make a backup onto tape, pull the tape off the drive and put it in a safe place - and there's nothing the hackers can do to it as long as you pull the physical plug/ring/etc that allows the tape to be written (in other words, you turn the tape into read-only). 

The single biggest error I see health care facilities making is no air-gapped backups - so when the ransomware hackers strike, there is no "disconnected" version of the files. If I were running some of these outfits, I would disconnect the systems from the 'net, clean up the infestation (possibly doing a clean install of the OS and applications), and then roll the backup off of the tape(s) to re-create the system. It might take hours to do, but when I'm done, I can flip the bird to the ransomware attackers and then publicly invite them to osculate my muscular buttocks - because I have my data somewhere where they cannot touch it, and they're not going to get so much as a plugged nickel out of me.

Air gap backups - the simplicity of being able to keep a read-only media offline so that the hackers cannot mount it from wherever they are - it's technology straight out of the 1970's.