Roger, obviously you have spent no time with these musical instrument tuners. I have. They are so sensitive that they can show variation in pitch that is really hard to hear. The one I have is a rack mount unit and can show a deviation in pitch of one whole note over nearly that entire width. Its when you get to the center that its hard to hear what its telling you.
It is a fact that some people hear pitch better than others, but from what you are saying, none of this has any bearing on your 'phenomena'.
So: we still have an unquantifiable phenomena, no math to support its existence (whereas there is math to support the existance of anything else real in audio). On this point I should point out that as a manufacturer I have heard plenty that did not seem to show up on the 'scope- until I got a better scope that is... and while I agree that test equipment comes well short of what we hear, it is only because it is measuring the wrong things, not because those things can't be measured! They all do, after all, exist within the medium of electronics.
So it can't be measured, no math, no proofs of hypothesis nor any sought, if I get the previous posts, the pitch variation so slight as to be well below audibility, therefore the 'gain variation' caused by an amplifier's distortion is also too slight to be audible or measurable (since in any amplifier the gain is something we **do** measure)... conceded by a comment about 100th of a db (or less), and apparently, other than listening, no other way to explain that this is the right hypothesis. IOW, because an effect is heard, therefore it **must** be Doppler Effect! -and can't possibly be anything else...
Occam's Razor is still suggesting a simpler explanation: the whole thing is a made up story and the actual truth of the matter is something far simpler. For example I know that slight tonal enhancement at certain frequencies can cause the image to jump out, and we are talking here about 'Doppler Effect sensors' that are sensitive to a '100th of a db', yet the effect cannot be measured by any test equipment- but it can by the 'special' sensors! So I will point to this as another glaring contradiction.
If it were me, and in the face of the Occam's Razor, the amazingly far more complex explanation I knew to be the right one, I would have hooked these 'detectors' up to some sort of device to measure their output (they are affecting the circuitry in the audio path anyway, so they have an output...). This has not happened, and yet is the blatantly obvious thing to have been done a long time ago, and I think the explanation for why that has not happened is also obvious.