Not necessary, because the author’s reasoning isn’t based on what will empirically be shown about medical patients’ predictions. The reasoning is based only on an analogy. That analogy happens to involve an empirically disproven belief, but the fact this belief was empirically disproven isn’t part of the point of the analogy. What matters is that the belief was false, not that it was shown to be false through empirical data.

Necessary, because if it were not true — if patients’ predictions of sudden changes in their medical status are NOT less likely to be remembered when those predictions are incorrect — then we have no reason to think that a biased memory is what accounts for the claim that many patients can predict changes in their medical status. If (B) were not true, the analogy regarding babies and full moons is no longer relevant to the conclusion.

Not necessary, because the author’s position is merely that we should doubt whether patients have an ability to predict sudden changes in their medical status. The patients may or may not be serious about their predictions; regardless, those predictions are not based on actual ability to make correct predictions.

Not necessary, because the analogy only requires that babies NOT be MORE likely to be born during a night with a full moon. This doesn’t imply that the babies are LESS likely to be born during a night with a full moon.

Not necesssary, because even if this idea IS a widely held belief, the author can still try to argue that we should be skeptical of the belief based on an analogy to a different belief. How widely held the belief is doesn’t impact the reasoning of the argument.