Well, I decided I was not even going to try to figure out how what had come to pass actually came to pass. One thing that my partner does not seem to understand is that without some sequence of events leading up to something it's almost impossible to determine exactly what happened.
I first tried just uninstalling Office 365, which was shown in Programs & Features alongside Office 2016. After uninstalling and restarting the system, when one invoked Word via the desktop shortcut the splash screen for Word under Office 365 still appeared. At that point I uninstalled Office 2016 as well.
Then downloaded Office 2016 via setup.office.com using the original product key and reinstalled it. We're back to normal. Heaven knows how long it will last, but this time it looks like the license key is now associated with his Microsoft account, and it had not been before.
Essentially a "nuke it and start all over again" fix. I hate those, but sometimes expediency wins out.
