I'm unsettled that a strategy involving using information that must have 0 correlation to each person's own correct answer could yield a collectively correct answer. I have heard problems similar to this before where I have been able to say "oohhhhhh" and find out why the answer does not seem to violate other overarching truths, but I'm not there with this one yet.
This is a like a person spelling out, step by step, how to build a perpetual motion machine, with no clear missteps, and the machine works, and I'm trying to understand how it jives with the second law of thermodynamics.
Then how do they arrive at a correctively correct answer? I'm reconciling this by noticing that there is no possibility of them both being correct. That is, their strategy effectively divides up the answer space such that they are covering all two possible correct answers.
What the strategy can influence is the correlation between Ava being right and Bob being right.