To chas_m,
Thanks, I had eventually thought of that, too. Separate users, BUT a single computer. So I deauthorized the computer for both accounts and rebooted (zapping PRam - it's an old superstition/habit when trying to make a problem go away.) Then I logged into the Apple account with the problem and authorized the computer again.
Same result.
I've got an email into Apple Support. If I find out anything useful to anyone else, I'll post it.
Thanks, again.