The speculation I read in that thread was basically that if ripped properly into the .NES format, you would wind up with identical versions (for that game, and many--but not all--others).

No. NES files as used today contain a few dozen bytes at the start which are used to tell emulators a little bit about the type of hardware that needs to be emulated. This header appears in the ROMs that Nintendo is selling. Nintendo would not have invented precisely the same header as is used by unofficial emulators by chance.

Note that no one is claiming that this is illegal on Nintendo's part.

Nobody's suggesting that they chanced upon the same header. That's ridiculous. The suggestion is that they're using the same tools to rip the ROM, and/or they're just re-using the format because it's a pre-existing format that does the job.