The date is 25/09/2017 07:59

I found doc on the self-locking feature that is tied to the gearshift
and moving or not and that has some four options one of which is "off"
but that has no bearing on locking when ignition is off unless there is
a failure in the system causing a spurious locking action.

It appears to be a stock 2005 Camry LE automatic with none of the fancy
options.

I saw in the owners manual on page 31 the "theft deterrent system" but that
simply describes the alarm if a door is opened when it's already locked.

On page 25 it talks about what you said, which is that it can lock all the
doors when the car is in motion, where this car, I think, does to that
because the doors are always locked, annoyingly. I never understood this
car-in-motion locks because we don't live in a place where someone is going
to carjack us while we're moving for heaven's sake. It seems like a lot of
scared people are out there who are afraid of everything.

On page 23 of the owners manual there is something about the power door
switch and "resetting" something, but I couldn't make sense of it.

If someone has a 2005 Camry, maybe they have the secret decoder ring?