That's probably what the author was thinking in February 2022 when they removed the batteries from their keyfob and only used the metal backup key, only to have the problem resurface less than a year later. It's probably safe to say that without batteries, the fobs were having no effect on the keyless system housed within the car.
Maybe the keyless entry computer stays awake to try to sync with a fob and then sleeps on success? If a user chooses not to use a fob at all, maybe it stays awake indefinitely trying to find a key to sync with.
Yeah sleep-wake problems often are related to things missing or broken in the (poorly constructed) system.
If the software on the car was poorly written, it may not have had a good back-off on the fob check, or if the fob itself was malfunctioning it may have left the car in a weird state.
While I wouldn't expect a fob to drain a car, it certainly doesn't seem implausible, especially given what the fix is.
My conjecture: there is ambient RF noise on key fob's frequency (most likely 315MHz), which is causing the key fob receiver circuit to remain active and process any signals that it receives, rather than going to sleep and periodically waking up to check for incoming transmissions.
Thinking this through a little bit further, I am wondering if subsystems can wake up if someone else uses their fob but the key signal doesn't match. Surely, at some level, something has to wake up to validate this.
Back when I was commuting there was an older subaru I always parked near in the parking garage that, whenever I unlocked my newer subaru with my fob, it’s alarm would go off. I sat there one day and did it over and over again, so it was definitely casual.