Okay, there seems to be only one answer.

The behavior I described was very consistent across many tests and many hours, and when I searched for an answer all I could find was people telling me: this is impossible!

Well, I finally revisited it, and tried to reproduce it, and it doesn't work anymore. I haven't been able to reproduce this behavior.

So, the answer seems to be, if this happens to you, reboot, cross your fingers, and hope it goes away.

Apologies to all of you who were as frustrated with me as I was frustrated with you.