Yes, counterfactuals do exist in some of Perplexed examples. There are alternative universes where Earth does not have a moon, or it does have a moon but it was not formed by a collision with a planetesimal. However, in this universe, the one we are observing now, the moon either was or it was not formed in such a way. There is no middle ground. Finding evidence consistent with the theory does not make the theory truer or more likely - what the evidence does is supply us with criticisms of rival theories.

CR is not independent from physics, nor can it be. The laws of physics entail the existence of universal computers and of universal knowledge creators. As David Deutsch has shown, there are deep connections between multiversal quantum physics and the theory of information. If Cophenhagen should turn out to be true it would impact on many things and not the least of which would be CR.