Altimeters and air pressure variation

At sea level, the change in atmospheric pressure with altitude is
close to 1"Hg/1000'. Logically, this would mean that the air
pressure would drop to zero somewhere not much above 30000'. It
doesn't, because as the density drops the variation with
altitude also changes.

Which brings to mind the question, how does an altimeter deal
with this? As far as I know, it's just a simple aneroid barometer
with a bunch of linkages and gears to turn its expansion into
pointer movement.

My altimeter is marked "accurate to 20000' ". Is this why? Do
altimeters for higher altitudes have some kind of clever
mechanism to deal with the non-linearity of pressure at higher
altitudes.

I asked my acro instructor (10K+ hrs, airforce instructor pilot,
ex U2 pilot so should know a thing or two about high altitudes).
He explained the non-linearity of pressure to me but was
stumped on how this translates to the altimeter mechanism.

Anyone know?

John