Ok having found the correct Uno Rev3 schematic and experimented a bit more it's clear that the led is driven when PB5 is set as an input (tri-stated), presumably because the LMV358 that drives the LED in that situation.
The question is still somewhat the same though: is PB5 getting tri-stated on power-drop, or does the Arduino tend to restart once on it's way down (so to speak). I think the latter is unlikely because in one case I'm controlling Arduino power with a FET which I think should turn off pretty fast. And the mechanical switch can be fast too. But still I wonder.
Also I don't understand the Uno rev3 schematic (https://www.arduino.cc/en/uploads/Main/Arduino_Uno_Rev3-schematic.pdf) entirely near the LMV358 that drives the LED. It seems to show something like 'L13' at the op amp output, but I didn't find any
other signals with that name on the schematic. Is there anything connected there, or is the amp just being used as a buffer?