The statements are equivalent if only a tiny fraction (tending to 0) of random reversible circuits satisfy P(C). We think this is very likely to be true, since it is a very weak consequence of the conjecture that random (depth-~O(n)) reversible circuits are pseudorandom permutations. If it turned out to not be true, it would no longer make sense to think of P(C) as an “outrageous coincidence” and so I think we would have to abandon the conjecture. So in short we are happy to consider either version (though I agree that “for which P(C) is false” is a bit more natural).
The statements are equivalent if only a tiny fraction (tending to 0) of random reversible circuits satisfy P(C). We think this is very likely to be true, since it is a very weak consequence of the conjecture that random (depth-~O(n)) reversible circuits are pseudorandom permutations. If it turned out to not be true, it would no longer make sense to think of P(C) as an “outrageous coincidence” and so I think we would have to abandon the conjecture. So in short we are happy to consider either version (though I agree that “for which P(C) is false” is a bit more natural).