What to your mind is missing from the analysis?
FWIW I circulate among a lot of geekier, tech driven photo industry people, and the Nikon shooters among them universally praise HE and HE*. I haven't seen an example yet where image degradation has been a problem among them. If I were looking to shoot into a sunset, or needed the absolute best image possible when shooting with a very fine gradient, I might switch out of HE*, but I look forward to testing even these situations. If/when I do I'll report back.
If you go back to what I said in my post:
"According to Nikon, there is a small loss in quality between normal Raw and High Efficiency Raw, when measured in the lab, but is unnoticeable in day to day use. But with HE*, although files are smaller again, you may notice a small quality difference."
This suggests to me that "I" am unlikely to notice any difference between Raw and High Efficiency. And, if I notice a difference between HE* and normal Raw, it's going to be difficult (outside a lab) to pin this down as resulting from using HE*, or being from some other reason.
So, for someone to find the differences that Nikon refers to, in my mind, would need a perfect experimental technique, and knowing where these differences that Nikon refers to, are likely to occur.
Now I don't know what that technique should be, but I don't see it including converting Raws to DNGs, admitting that the lighting might have varied between test shots, and using PNGs for a comparison.
It's the sort of thing I might do as a rough-and-ready comparison to see if,
for my photography, I am likely to see any meaningful difference, but I am happy to go along with what Nikon has said. Especialy, as I'm not concerned about file size, so it isn't an issue for me.
If I felt the need for smaller file sizes, e.g wildlife where I may use high fps, or if I were an event photographer, I would probably do a simple comparison to confirm that in my circumstances I could just accept Nikon's assessment.
However, I couldn't be bothered with the effort required to do a statistically sound comparison (I taught statistics and experimental design at University), and to be frank, I don't have the expertise to design, or carry out, or analyse or interpret an experiment that could disagree or confirm in any meaningful way, what Nikon are saying.