Aha! If it is true that events are time stamped according to when they were reported to the cloud, rather than when they actually occurred, then it explains everything that I observed.
I didn’t mention that my home has emergency power, but for only some circuits; it comes on when an outage lasts more than a few minutes. When I saw the reported behavior from Rachio, which seemed to indicate power-on at the time the outage ended, I figured that the controller must be plugged into the wrong circuit. But now I have double-checked and the circuit does receive emergency power.
So, what really happened is that the controller lost power only briefly and came on again in time to run its regular schedule. However, it had no Internet connection, so it ran the schedule without regard to weather. (The loss of Internet connectivity is Comcast’s problem, not mine; my modem and router are on UPS and did not lose power.)
I will enter a feature request to time stamp events according to when they actually occurred. The current behavior is very confusing when trying to figure out what happened.