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The episodes is very well scripted; and in fact, refers back to the episode from the original Star Trek where Kirk finds himself in a parallel universe.
However, what is the probability that in parallel universes there would be so many people who were so similar? Slim to none. Butterfly effect. Chances are even a tiny difference at the point of divergence would create most things different and not related. Similar people existing would occur one in millions, if that. But, also, however, that would lead to a dull story!!!