It finally happened! I bought a new humidifier, which for no reason includes an IR remote control. That IR remote control uses IR codes which overlap with my (2011-era) AppleTV.
I knew overlapping IR codes happened, and have been frankly surprised that they have never happened to me in my lifetime, as far as I know. Well, lightning finally struck.
(Problem was resolved using masking tape, because I couldn't find my electrical tape. It took 4 layers to mostly block the signal, and 5 layers to fully block it. Apparently masking tape isn't so good at masking IR...)