First let me say that I am never comfortable with denying what a listener hears, so if a 16th of an inch speaker movement has an audible effect, then I’m personally perfectly happy to accept that it indeed has a audible effect.
But I would apply some logic here. First, it‘s reported that the sound difference can be heard when walking into the room, so there‘s no relation of the speaker movement to seating position. Second, 1/16th of an inch represents 1/214,375th of a second in terms of the speed of sound. Third, even minor head movements would have similar effects to moving the speakers 1/16th of an inch, so theoretically the timing of instruments would be constantly changing even if the listener was trying to sit perfectly still. Personally I can never sit still while listening to music.
So let’s look at the facts. With a tiny movement the sound is changing and the changes can be heard everywhere, but such tiny movements are very unlikely to affect speaker performance from a spatial standpoint. So what constitutes a good alternative explanation? My guest is that nudging the speaker….literally bumping it with the hand is causing the speaker footers to move slightly across the floor. As soon as the speaker reaches a point where all 4 feet are in more perfect contact with the ground (equal pressure on all 4 feet) vibration will be reduced and the overall performance of the speaker will improve. I can perform a similar trick with a piece of paper under one foot of a TT, CDP, Amp or even a PS.
Shimming any of the above to ensure all 4 feet are in perfect contact with the support platform can have a profound affect on the music.
So I would believe that rather than it being the repositioning of the speaker spatially that’s making the difference, it is perhaps the fact that minute differences in the floor are providing better/worse contact between the 4 supports of the speaker. All it would require would be a few thousands of a millimeter to hear a substantial difference that would address all the observations.
Just to mention, I used to use a stethoscope to check the contact between spikes and spike cups of my Magico speakers. Spikes that would ‘feel‘ as though they were in perfect contact often weren’t. Using spanners to tighten spike locking nuts nearly always introduced minor maladjustments.
So just a thought regarding what may be going on.