I am still struggling to reconcile that with what I
have read about wild bees.  My understanding there is that a newly
established colony will start during swarming season at the top of the space
they have chosen to occupy and build down.  The brood is always at the
bottom, and as the nest moves down the comb above them is filled with honey.
During the winter, I understand, they will eat their way back up again so
that by spring they are once again at the top and working their way down.

Have I got that wrong?  If I have it right, why do bees in hives want to go
up if bees in hollow trees (etc) want to go down?

This is precisely what one would expect them to do and it confirms all that
you have been told by experienced beekeepers.
When a swarm occupies a hollow tree, or a hive body for that matter, that
has NO COMB OR foundation, the first thing they do is build some.  They
start from the top, and build down.  They fill the first cells ( at the top
) with brood or nectar, (I do not know which), and as more comb is completed
(going down), they fill it also.  when they get to the bottom, (or what ever
depth the comb happens to end up being), the queen will continue to lay eggs
there, and as the brood above hatches out, it will be filled with
nectar/honey/pollen.  This will continue until winter, when the colony moves
up, consuming the stored food.  (leaving the bottom empty)
If you put bees on drawn comb, they will store their food above the brood,
just as you have been told.  It is when a swarm initially has to build comb,
that the reverse may happen, temporarily, until enough comb has been built,
and the brood hatches out of the upper portion of the comb.

In the last part of your statement, if the winter has been mild enough for
the colony to consume all the stores at the level they are at, that is if
they are able to move to  the food, or move the food to the cluster -
horizontally, then, in the spring, the only choice they have is to go down
(there is no more "up" in the hive, they are at the top)

Roekel