I don't understand why you can't see that is plainly untrue to the naked eye in the unaltered detail images I posted above.
I am using the images you posted above. They are very good. And I jumped to the same conclusions you did when I first looked at the coin. It wasn't until I overlaid the images that I could see their "identicalness" (if there is such a word). I agree. Seeing them separately, they look different. It is the overlay that reveals their "identicalness".
The bottomline is that most likely no TPG would certify this coin. You cannot see the die chip in the upper loop of the S and the VDB is obscured by a worn/damaged rim.
Stop and rethink what you just posted. Overlays are problematic when you didn't create both images yourself, especially when one or the other image is as imperfect as the OP's. You don't even have a full circumference of the obverse to base size comparisons on, and given the radical difference in wear there's very little else you can trust. At least the full circumference can be assumed to be relatively close to original. Except for the fact that it's in a container, and not lit brightly enough for you to actually see the true edge of the rim. So you're making subjective judgments regarding size relationships, not even factoring what I've already mentioned about tilted macro images distorting perspective. And it should be intuitive that additional layers of processing complexity offer additional chances for error. And remember, I had to blow up the OP image to 400% and the Heritage image to 150% to get a SWAG size similarity large enough to post here. How much error did I introduce myself there? You're overthinking. Trust your eyes, not your image processor.