12v battery charged by traction battery while off?

I've been having a discussion with someone who claims that the 12v battery gets charged by the traction battery even when the car is fully off. My experience is that when the car is off, it's off. When the "Ready" light is on, then the traction battery will charge the 12v battery.

This is based on my experience of:
1) Having the headlights on overnight, which caused a low battery alert (below 11.8v).
2) Forgetting to turn off the overhead lights overnight, which drained the 12v battery so far nothing worked. I had to charge it a bit before the car would start (the 12v needs only enough to run the electronics, the traction battery then starts the car).
3) Plugging in a 12v refrigerator on a camping trip, which drained the 12v battery enough over three days that the low battery cut-off in the refrigerator shut the refrigerator down, and food had to be tossed, but the 12v had enough to start the car.

Question: Do some versions of the Prius (later Gens) charge the 12v from the traction battery while the car is fully off? I don't think so, but I may be wrong.

 

Thanks. That's what I thought.