Unfortunately, that article misstates the relationship between ISO values. Powers of two are actually precise steps based on the cube root of 2, just like 1/3 step increments for aperture or shutter speed. They are only rounded off for the convenience for labeling lenses or shutter speed dials.

For example, lens apertures are rounded off from the series: 1.41, 2.00, 2.83, 4.00, 5.66, 8.00, 11.31, 16.00, 22.63, 32.00 … But they are conventionally labeled: 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32 …

ISO values are actually: … 31.50, 39.69 50.00, 63.00, 79.37, 100.00, 125.99, 158.74, 200.00, 251.98, 317.48, 400.00, 503.97, 634.96, 800.00… But they are conventionally given as: … 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 640, 800…

And fractional shutter speeds follow the same series and convention as ISO values but expressed in the denominator as 1/30, 1/40, 1/50, 1/60 …

So equivalent offsetting incremental changes in ISO, shutter speed and aperture should result in precisely the same exposure for the same lighting. But errors in actual shutter speed performance or imprecision in lens aperture adjustment (and possibly even sensor response) might produce slightly different exposures.

Yes, but it acurately discusses how cameras get to that result and the issue is that these multipliers are not all implemented in the analog domain so the camera uses the nearest analog result and then pushes or pulls the result to the specified ISO. This does result in the expected exposure but it can differ in noise and both highlight and shadow detail for images that are subsequently processed further.

In the case discussed in this thread, one would expect that post processing (auto lighting for example) will get differing results at some ISOs than at others even if the unprocessed shots are equivalent

After some further thought I believe I have the answer to this mystery ... When I said it was shot through a screen door, that was not entirely accurate, it was actually a screened security door.

The security part of the door has fairly substantial diagonals that 'grow' and expand until they blur away to invisibility as the sign is brought into focus.

Now, as this was a hand-held test, and the diagonals are not visible through the viewfinder when focussing on the sign, there can be no guarantee that these blurred diagonals are in the same locations in both shots. That is, the loss of shadow detail can be explained by the diagonals obscuring some portions of the scene in one shot but not the other.

Here is a 100% plus shot of approximately the same thing shot with a 70mm lens, but with the focus being the screen instead of the sign