I'm curious, did you attempt to turn the second ring before the third? And did the third ring move the objective itself, or did you have to loosen it and then manually rotate the objectives? My assumption of there being 2 rings after the outside retaining ring would be that the innermost would be an objective retaining ring and the "middle" one would rotate an entire lens cell. The reason there are multiple rings is, presumably, because these binos are nitrogen filled, and loosening the objective retaining ring, whichever one it is, would likely release all of the internal nitrogen. So a nitrogen-filled bino with eccentric objectives most likely requires, at minimum, an objective retaining ring, a means to rotate the objective lens cell without having to loosen the objective retaining ring, and a lens cell retaining ring. The lens cell retaining ring must be the outermost, and I would guess the innermost to be the objective retaining ring and that you would not want to touch that one if you don't want to release all of the internal nitrogen.
Of course, there's more that one way to skin a cat, and there's more than one way to design eccentric objectives for nitrogen filled binos, so you may not have released the nitrogen. However, in the design that I've seen before, you probably would have done so if you loosened the innermost retaining ring. If this post gives you pause, you might consider going through with the exchange still. You did, after all, pay for a collimated and nitrogen-filled bino. You didn't receive the former, and may or may not have the latter now.
You've given more deep thought to this than I have

Now I'm going to give you a chuckle... you may wonder how it relates, but I have a short haired Lemon English Pointer (see avatar). Well, I took a single short hair shed by the dog and purposefully put it in the middle of the objective glass that I was working on. If the hair turned while I was using the adjustable pin spanner wrench, then the objective was turning. Neat trick huh? And afterwards I could just blow the hair away and have a pristine objective again.
Anyway, after removing the outermost objective casing and exposing the three-ring system, each with 1.5mm holes for a spanner wrench, I found that the initial ring I encountered did not rotate the objective when turned. Neither did rotation of the second ring after I'd removed the first. Only upon reaching the third ring did using the spanner wrench also turn the objective. I don't know if there was another ring under that one or not and I don't know if by turning it I let nitrogen escape. I'd like to think that nitrogen would escape only if I'd removed the objective cell from the barrel, which I didn't come even close to doing.... but then maybe turning the innermost ring could have released the nitrogen.... I'm not expert enough to know one way or the other.
But, anyway, it allowed me to achieve collimation. I had to do something because the binos just couldn't be used at all in the state of collimation they arrived in. Double vision was fierce and I was even getting eyestrain and the start of a headache looking through the binos.
If I let the nitrogen out, then fine. The learning experience was worth it and at least I can use the binos and they are a dream to use now. No eye strain at all and a perfect merged FOV.
I certainly don't want to put anyone off buying Oberwerk 20x80 Explore binoculars.... quite the opposite. These are tremendous binoculars for the money and their light weight and ease of use in a ZGC makes them worth their weight in gold. It is true that the binocular skin does not allow access to the prism collimation screws by the amateur at least, without marring the skin. But actually, I'd rather not adjust the prisms anyway unless it is absolutely necessary because there is a great chance of achieving collimation but losing light throughput. I much prefer objective rotation as the mechanism of achieving collimation if possible.... in my case it appeared to me that the prisms were well aligned as the exit pupils looked very normal and symmetrical. The only thing left to try was objective rotation and it worked for me after buying the adjustable spanner wrench using a pair of 1.5mm pins.
The nitrogen was a nice feature, but what caused me to buy these binoculars was their light weight. I don't think you can find a lighter pair of 20x80s on the market. And the optics are as good as in the Oberwerk 15x70 Explore, which is to say that they are great. I would say essentially as good as my Oberwerk 15x70 Deluxe which had been my favorite binoculars for a couple of years. Now I suspect my two Explore binoculars are going to get most of the use time in my ZGC.
Oh... I should add... Oberwerk was not at all remiss in not rushing me a replacement pair of 20x80 Explore.... they couldn't as they were having a stocking issue.... but they would have when they got more stock in place. I didn't know all that when I decided to take a hands on approach, but everything turned out fine and I am happy as a clam.
Rick