There doesn't seem to be a huge amount of research here. I'd like to read the entire study linked in the question, but don't have access to the full text through my institution. But I was able to find an article from the Ohio State University College of Veterinary Medicine that discusses it. To be clear, the study did not investigate carrying them by the scruff of the neck. It specifically recommends this as a form of restraint during veterinary checkups, claw trimming, vaccinations, and so on.
As a caveat, the study was also conducted at OSU so this is to some degree a PR piece, but the lead author specifically says he believes the technique is painless:
"Cats generally seemed more content, sometimes even purring, and less
fearful during veterinary procedures when clips were used instead of
restraint by some other means," Buffington said.
"It's easy to tell if you're hurting animals because they don't like
it when you do things to them that hurt," Buffington said. "When the
cats in this study saw the clips, they often would lie down. If the
cats were hurt by them, they would have seen those clips and tried to
get away. If anything, the effect on them is positive."
There's also this article, written by a vet, that discusses the study in more detail. It says:
The cats did not exhibit signs of pain such as tachypnea, tachycardia,
or mydriasis. Moreover, no significant changes in heart rate, blood
pressure, or temperature were observed in 15 of the cats that had
implanted telemetry devices. The researchers concluded that PIBI is
not a fear or pain response.
This all sounds pretty reasonable to me, based on my own experience with cats. I've known several that picked up pretty strong aversions to things they associated with pain or trauma, like the sound of heavy footsteps after having been accidentally tripped over. Even if they didn't associate the clip with pain in the future, they would certainly react fearfully once it had been removed, and it doesn't sound like this was the case at all.
The author of the study describes the pressure as roughly similar to a blood pressure cuff, and carrying no real risk of injury. So the idea behind the technique is not, as suggested in the question, to pinch the skin so tightly that the cat can't move. It's to take advantage of a reflex behavior that's useful for mother cats managing their kittens, and that many cats happen to keep throughout their lives. It seems really unlikely to me that a gentle pinch would be calming and painless as kittens, but then becomes paralyzingly uncomfortable as adults while evoking the exact same physical response.
On the flip side, the author does seem to have some affiliation with a company that sells a product to do this. I think, from looking at their website (which I'd rather not link to; it's in the second article), that it's sold to vets rather than pet owners. I'm not sure what the connection is or whether the study or idea for the product came first; the second article does mention that he donates all of his proceeds to one of OSU's cat initiatives. So this may be a significant conflict of interest, or the university may have licensed his clip design after the study and the company wanted him as an advisor. I could see where he might have become convinced by the research that this is a helpful technique, and thinks it should be easy for vet staff to use the technique in a consistent, safe way. Or it could be a money grab with peer-reviewed advertising. In any event, it would be trivial for another practitioner to try to reproduce the results of the study, so I'd be pretty surprised if they're that far off the mark.
Along with this, the American Association of Feline Practitioners and the International Society of Feline Medicine say, in their AAFP and ISFM Feline-Friendly Handling Guidelines, that there's some controversy around the technique among veterinary professionals. The guidelines reference the OSU study, so they are aware of its conclusions without completely adopting or rejecting them. They do also "strongly support the view that scruffing" -- which they distinguish from clipping -- "should never be used as a routine method of restraint, and should only be used where there is no alternative." ("About Scruffing Techniques", page 9 of the PDF.)
Personally, I'd like to see more research before I firmly say it's humane or not. I didn't see any direct responses to the OSU study, or anything else that uses the terms
PIBI. My instinct is to say that I don't see anything indicating that it's painful or traumatic, and on the surface it seems reasonable, but I having read all this I could still be convinced by a practicing veterinary professional in either direction.