Somebody with whom I am having a 'debate' has asserted
that there is an altitude-dependent error component

The distance to a station using DME is "slant range", the distance to
that same station using GPS is a projection, so some slight error is
introduced there. It is possible that your friend is mis-interpreting
or mis-applying this tidbit.

"Aircraft ... are using a map optimised to the GPS system and this is
the key point which seems to be passing you by."

There are several geoids in use, and the choice of geoid may introduce
position errors. A geoid is a surface of equal gravitational potential
(a "mean sea level") and is an idealized surface - the real earth has
bumps and wiggles which are modeled imperfectly (or not at all) in some
models. Your friend may also be mis-applying this tidbit.

Jose
--
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