Well, tried it Cheetah 6, but with the same result — see first image below. It's not identical, but close enough to make me draw the conclusion that
if seen in a reflection, HDRI supersedes other backgrounds.
The more I think of it, I think this is how it has to be, or HDRI would have no effect at all.
In fact, turning off HDRI gives me the intended floor-fading-into-fog effect, but also, of course, fog being reflected all across the sky (see left image below) which is exactly what would happen if HDRI took the backseat to fog. I guess to a surface, HDRI is basically "what to reflect when there is no other object to reflect", and fog is not an object.
So this is all my bad, or at least I think so. My brain still isn't sure it understand what it's talking about.
Which brings me to, though:
Here's a wild and un-thought-through idea: Might it be a potentially helpful feature if fog and HDRI could be set to
gradually supersede each other, so that a surface perpendicular to the sky reflected 100% fog and a surface parallell to the sky reflected 100% HDRI instead.
Without taking responsibility for all fathomable ramifications of course, at least in my scene that would provide a gradual dissolve from fog/ground to sky in the ball, and full fog in the vertical surfaces of the polyhedron, sky on top, and fifty-fifty in the slanted ones.
Perhaps that would introduce other problems — but a thought here is it would help get rid of the sudden sharp edge where fog is overridden by the HDRI image.
See below for a mockup (courtesy of Photoshop) of what that would look like in my specific scene. But whether that would be applicable in any other situation is harder to think of at this time of night...
Can I file this as a suggestion?
Or should I just go back to my day job and stop thinking too much?