You have it exactly right Fred. Distort by default has some color distortion in the no-op case. It is however as you can see by your results, around 1/2 that of a 8 bit color value. Very minimal.
Distort uses a 2 dimensional Elliptical weighted average for re-sampling. The default filter Robidoux (a professor who is a regular of these forums) calculated it to be minimal color distortion for NO-OP. It is also very close to a Mitchell-Nevel resize filter (whcih also has slight color mixing in no-op, but is common for resizing images). However it looks like it has been proven to be impossible to use a 2D re-sampling filter and get no distortion.
To remove distortion in no-op case use
-filter point turns of EWA re-sampling, and go to the fall back of interpolative color lookup.
-interpolate then can be used to set what type of interpolation (bilinear by default). However interpolations will produce sever aliasing effects on compressions of more than 50%, which is common in most image distortions (and thus why it is NOT the default).
Note that some interpolations also has color distortions in No-Op case too. Spline for example has a rough .65 sigma Gaussian blur of the pixel neighbours.
For more information you need to understand image distortions (which includes resizing images). See the introduction to distortions in IM Examples. It also goes through everything I have discussed here.
http://www.imagemagick.org/Usage/distorts/
Also more specifically. No-Op Distortions...
http://www.imagemagick.org/Usage/distorts/#distort_noop
For rotating images without scaling, I would turn off EWA using
-filter point but I would also use
-interpolate mesh which was specifically designed for handling rotating images (and minimal scale changes), while better handling rotated 'edges'.
IM Examples, Interpolations, Mesh
http://www.imagemagick.org/Usage/misc/#mesh