If in the brightest zone we are "just quantizing noise", then
there is no visible image, at all.  We'd have a frame with no
detail at all.  Clearly we are quantizing a great deal more than
noise.  (What you mean is that the LSB of the digitized value is
noise.)

Because shot noise increases with the square root of the signal,
even considering the increased SNR in the brighter zones it is
indeed almost certain that a 12 bit linear encoder is over
sampling, and hence wasting bandwidth by recording useless
noise in the higher brightness zones.

The reason Nikon chose the particular curve they did was because
it is a fairly close match to the eye's perception, which is why
they say it is "visually lossless".  And in general it is.  It
is only in certain circumstances that the difference can be
detected. Nikon chose that particular compromise as opposed to
greater reduction in file size by reducing the probability of
over sampling even farther, or lesser reduction in file size by
retaining some likelihood of over sampling (and thus keeping
more of the useful data in instances where it is not over
sampling).

Here is another article that discusses it,

 http://www.nikonians.org/dcforum/DCForumID86/16055.html

with an interesting graph (explained in the above URL), at

 http://home.comcast.net/~NikonD70/NikonInfo/NEF_Compression_files/image002.gif

which shows how how closely the Nikon 683 encoding matches CIE
perceptual lightness.

Another discussion, using a 677 level format compared to a 12 bit linear
format,

 http://www.msss.com/http/near_cal/fs_algorithms/companding/companding.html

And I note your later article where you have discovered

 http://regex.info/blog/photo-tech/nef-compression

which makes an (over dramatized, IMHO) attempt at a graphic
visual representation of the differences between NEF and
Compressed NEF formats.  (Sometimes graphing noise distribution
is interesting, and certainly mathematical analysis is too, but
I just don't see where it generates a useful image to look at
error signals.)

If one format has, in zone 0, 2048 values, while another format
has only 160 values, what is the result of a comparison between
formats if it is done the way you describe?

First, what will be seen depends greatly on the images.  Your
description of "had detail in all brightness levels" does not
necessarily mean it would show a significant difference.  If,
for example, the detail is high frequency and of sufficient
amplitude, the difference between the two formats would be
almost negligible.  If it is lower frequency and of small
amplitude, the errors might completely hide the detail.

For example, if a tonal gradient rapidly goes from one limit of
that zone to the other limit, there are only two values of
significance.  Relative to the start of the zone, 0+ and 2048+
for one format and 0+ and 160+ for the other format.  The
quantization error on the first format is 1/4096 of an fstop and
on the other is 1/320 of an fstop.  Which is to say that the
noise is small compared to the signal, and we cannot distinguish
the noise with our eyes.

If the tonal gradient has half the amplitude, the SNR is reduced
by half, because the possible error amplitude is the same.  If
there is a gradual gradient though, the SNR goes down even
further because the possible error again remains the same, but
the actual signal amplitude change from one pixel to the next
gets smaller and smaller as the rate of change across the
gradient is reduced.  At some point all that is visible is,
indeed, quantization noise.