Now, we've had that white Apple Remote for several years. The Apple TV is paired with a newer aluminum Apple Remote, and never the twain had met. Until now. Given that we've used both remotes separately for years, we must have hit some peculiar set of circumstances in which the white Apple Remote trained to the Apple TV. (I can't tell if the power outage was the culprit, but the command sequence to pair is "press and hold the Menu and Next/Fast-forward buttons for 6 seconds" — and I certainly didn't press that sequence!)
Then, while pausing, selecting menu items, and otherwise controlling the eyeTV software, I was also invisibly navigating the iTunes Store on the Apple TV and purchasing songs. The sequence of purchases then made sense: all M's — Mike Oldfield, "Mess Is Mine" by Vance Joy, and MisterWives. (No offense to the artists in question; I don't know their work at all, other than Oldfield.)
All that remained was to unpair the white Apple Remote from the Apple TV to get rid of the ghost in the machine.
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