You are right, they are different questions, but the straw man was not intentional, I thought the original phrasing was ambiguous enough that it could be interpreted in both ways ;)
In other words, it was unclear to me what the answer to the question "Are the assumptions part of the hypothesis?" was. If, as I did, we assume that "yes, they are" then I don't think it follows that the probabilities will both be `1`, because we do not have logical proofs for the claims, the implication could only be true in the model (they are not necessarily entailments).
The waters are muddied further still when the hypothesis itself is phrased as an implication.
EDIT
It also strikes me that for your line of reasoning to hold, it is not sufficient that Pd1 = Pd2 are small, but instead `Pd1 = 0 = Pd2`, in order to justify this line:
In other words, it was unclear to me what the answer to the question "Are the assumptions part of the hypothesis?" was. If, as I did, we assume that "yes, they are" then I don't think it follows that the probabilities will both be `1`, because we do not have logical proofs for the claims, the implication could only be true in the model (they are not necessarily entailments).
The waters are muddied further still when the hypothesis itself is phrased as an implication.
EDIT
It also strikes me that for your line of reasoning to hold, it is not sufficient that Pd1 = Pd2 are small, but instead `Pd1 = 0 = Pd2`, in order to justify this line:
Which is tantamount to saying Is it not?EDIT (2)
Ignore that, it is not tantamount, it is a weaker condition.