I have stated how the Nimitz case is quite exceptional in how it has survived closer scrutiny. The Coyne helicopter case is not like that. There seems to be a lot of reasons for doubt, especially because of statements Coyne himself has apparently given. As a result, it's hard to make sense what actually happened.
It's best to begin with the original reports as signed by Coyne and the other 3 witnesses. As for those other claimed witnesses, quoting Philip J. Klass:
Volume 53 - CSI
Here are the reports of the crew:
UFOs - Documenting The Evidence
Text for the interesting part as copied from ATS:
The Coyne incident, Mansfield, Ohio, 1973, page 1
Note that the report only states the altitude had unexpectedly changed, not specifically that the UFO had lifted it. It also doesn't mention any effects on the compass, as has been reported later, which seems to have been possibly faulty before and after:
Volume 53 - CSI
All the distances and speeds of the object seem to be just visual guesstimates. As for the problems with the radio:
Volume 53 - CSI
As for that green light:
Bad UFOs: Skepticism, UFOs, and The Universe: New : Historical UFO Documents (Klass, Hynek, others)
The descriptions given by Jezzi, who was sitting in the front on the other (left) side, give further hints that may be the reason for the color:
That already raises question how much they actually saw, and it only gets worse:
http://www.debunker.com/historical/PJK_Coyne1976.pdf
So, it's not just those general problems of human imagination and people seeing stuff that's not there, but Coyne clearly thought it could have been something much more mundane. Even this:
While Fravor has been consistent and clear that he "knows what he saw", based on those comments, Coyne didn't.
I believe this is the critical part that made this case so famous:
First of all, that rate of climb is well within the capabilities of that helicopter, with "Initial Rate of Climb: 1,600 ft/min":
Bell UH-1H Iroquois | Royal Australian Navy
So that climb does not actually need anti-gravity or anything exotic, all it needs is someone having kept the controls in the wrong position. Can a professional pilot do something illogical with the controls in a somewhat confusing situation? That's what happened to Air France Flight 447:
Air France Flight 447 - Wikipedia
That seems like a very elementary and stupid error, and they barely found out what happened before it was all over, and the culprit didn't seem to understand it at all.
So that's the situation with the Coyne case, there seems to be little information that could be really trusted, and no actual evidence. And even if it happened more or less as has been described, no anti-gravity needed, normal capabilities of a helicopter suffice.
Remember there are physicists like Puthoff who believe things like remote viewing, scientology, measuring feelings of chicken eggs with an E-meter and so on.
I have some leads to follow as for who that physicist might have been. Haven't had the time to check those out properly yet. My first guess would be that it was a physicist employed by the DIA (AATIP was a DIA project).