One information does not need to exclude the other. Both is important. However, you can more appropriately preserve 'operators manual' by scanning it to PDF, and (re)print later if desired. Words and pictures, wiring schematics, none of that needs to be emulated, it does not really belong in _software program.
Emulators emulate electronic components, chips and integrated circuits, so that "software" (game ROMs in this case) can run on some other computer even when all the original hardware rust to dust, which is the motivation to preserve this and also the reason why preservation is done by *emulation* rather than with pictures, diagrams and descriptions.
Yes, that's what emulators do, but MAME can easily document it both by simply not initializing the 3rd button as "default" wiring/'mapping, BUT leave the pin still listed in the control panel with the rest, where you could virtually wire it, just like you could practically wire it if you had the real PCB. -- Once your emulator hardware can do anything actual hardware can, then you can say your emulator is done, it fully and properly documents the original hardware.
As if there is some danger of having too much information?
Can you think of it as "Easter Egg", a gift programmers left for curious operators to have fun, or whatever the reasons are they put those eggs in today's games, eh? -- What if this 3rd button technically qualifies as the first "Easter Egg" in gaming history, and you would have it forgotten in favor of some 'operator manual'? They do not document "Easter Eggs" in game manuals even these days, do they? You have to FIND it, which is what makes it even more cool, right?