Hi Tom,
wow.
You do have a background in mathematics, right? I’ve tried to get the definition of mean and median error but there were only equations and i got bored. Could you explain the two to normal people? 
Anyway, it does make sense the way you explain it. That would mean two things:
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The quality of the alignment is determined by the images and not by the Max Repro Error.
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The Max Repro Error is only there to basically filter the worst points out of the cloud, which would impact the meshing more than anything else.
This all goes with a loss of the overall number of tie points, for good or bad. It would be great to have that curve available, so that one can estimate at one glance where to lop off the top.
Apart from that, there is one thing I want to add. The errors are definitely influenced by exif grouping. With grouping on, they can be worse (especially with change of focus and/or aperture at the same focal length) but the chance for a proper alignment and all or most images in one component is much higher. Switched off again, it usually decreases by about 20% in my case, which is due to slight adjustments that can then take effect.