Actually my revised opinion, as expressed in my reply to Tyrell_McAllister, is that the authors' analysis is correct given the highly unlikely set-up. In a more realistic scenario, I accept the equivalences A~B and C~D, but not B~C.

I claim that the answers to E, F, and G should indeed be the same, but H is not equivalent to them. This should be intuitive. Their line of argument does not claim H is equivalent to E/F/G - do the math out and you'll see.

I really don't know what you have in mind here. Do you also claim that cases A, B, C are equivalent to each other but not to D?