OK, thank you all for your suggestions.
I'll state right up front I have no clue WHY this was happening. That said, I did find a solution:
Using DISM to do an on-line refresh of system files.
Opened an elevated command shell (I used powershell, but cmd works as well)
DISM /Online /Cleanup-Image /CheckHealth
Followed by sfc /scannow
I had to run this while logged in as each user that was experiencing the issue on this workstation.
I suppose a fresh install of Windows would also have taken care of it, but this was easier, and didn't necessitate reinstalling all the user's applications.
Hope this helps others who run into this problem in the future