With the bare minimal force required to not drop it, Rita
holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.
If there were different universes,
this would be placing the same pole of the magnets against each other, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.
Since this won't happen,
we know Joe's conjecture is false.
Joe might argue that Law 7 still explains this.
Strong enough magnets to demonstrate the effect without actual surface contact negates Law 7. My kids have fridge magnets strong enough to do this, and a good few of my souvenir magnets also qualify.
Rita's force in holding the magnets, too, can be eliminated with little difficulty with suitable application of string, making the magnet strength required to show the (absence of) effect quite minimal.