I also found this article by Michael to be contoversial and its conclusion misleading with regard to the way we use DoF in our photographs.
For example, often we use a shallow DoF to make objects in the background less distracting.
In the update to this article, which is a response to a reader's question about using a 300mm lens (from a greater distance) instead of a 200mm at f2.8 for shooting skiers, Michael safely offers the advice that the 300mm lens will provide exactly the same DoF as the 200mm lens.
However, in my view, if the intention of the photographer is to remove as much distracting detail as possible in the background, the longer focal length is a better choice.
If the reader's question had specified different lenses, for example, if the question had been, "I normally use a 300mm lens at f2.8 to photograph skiers, but next Saturday I've been offered a prime viewing position which is much closer to the action and which will allow me to fill the same amount of the frame (with a single skier) using my 85/1.2 at f2.8. Will DoF be the same?", I think Michael would have hesitated to answer in the same way.
The fact is, using the 85/1.8 for the same shots, would have introduced the risk of all sorts of distracting background skiers being visible and more prominent, not only because the background is more extensive (wider FoV) but also because smaller images (secondary skiers) would 'appear' sharper because they are smaller, yet retain the same absolute resolution as the blurrier looking objects (subjects) in the 300mm shots.
Nevertheless, we have to thank Michael for pointing out this phenomenon, that although a background object might look blurrier when using a longer lens from a greater distance, the actual detail in that blurry object is approximately the same as the detail in the smaller, and therefore sharper looking, object in the wider-angle shot taken from a closer distance.
I didn't know that when I first read this article. Of course, being a natural skeptic, I had to check this out for myself, and sure enough my own tests demonstrated that it is approximately true, but not precisely, as the OP's comparison demonstrates and as Olaf has mentioned several times.