Norton 360 back-up and separate hard drive query

I have a query regarding Norton 360 back-up.

I recently helped a relative 'revive' a laptop where an upgrade to Windows 10 had gone wrong.  We got it fixed the laptop is working  again.  They have Norton 360 installed using one of my spare licences  and we had to download Norton again and reinstall it, which was also done OK.  They have a detachable hard drive which they use to keep the Norton 360 back-up files on.  Prior to the upgrade attempt they also used the drive for a manual back-up, simply copying files across from the laptop hard drive.

When we got the laptop working again and Norton 360 had been downloaded and installed, I assumed that we would just be able to recover all files from the detachable hard drive using Norton.  However, when trying this, the reinstalled Norton 360 did not recognise there was an existing back-up on the detachable drive.  We therefore had to recover the files from the manual back-up that had been made prior to the upgrade attempt.

This has prompted me to question the worth of the Norton 360 back-up in the event of a catastrophic hard drive failure on my own machine.  I likewise have a detachable hard drive that I use to store the Norton 360 back-up files on.  If my PC crashes irretrievably and I need to get a new machine, I know that I'll be able to download Norton 360 to it from my account quite easily.  However, if I plug my detachable hard drive into the new machine and ask the newly installed Norton 360 to recover the data from it, am I right in thinking it will not be able to do so, because it did not create the back-up set?

Gary