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AlexSchell comments on Personal Evidence - Superstitions as Rational Beliefs - Less Wrong
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I don't really know much about this, but from what I recall the theorem doesn't require the hypothesis that info can be shared. The theorem says that two Bayesians with common priors and common knowledge of their posteriors have the same posteriors. They don't actually need to communicate their evidence at all, so the evidence need not be communicable.
In practice, though, how are they going to attain knowledge of each other's posteriors without communicating?
Actually, to agree on a proposition, they only need to have common knowledge of their posteriors for that proposition. (At least this is how Aumann describes his result.) And they can communicate those posteriors without communicating their evidence.
You're right, of course. It was wrong of me to confuse communicating their posterior with communicating their evidence.