This stopping rule problem is tripping me out!

Suppose I’m a second Bayesian, and I don’t see any of the data, just the hired statistician’s final opinion.  I know exactly what the hired statistician’s final opinion will be beforehand, so it can’t possibly give me any new information about the effectiveness of the drug.

So now I disagree with the statistician.  Why?  The statistician says, “I had all of this data, and I updated on it, and this is my considered opinion.”  And I say, “yeah, but I knew that would be your considered opinion, so updating on it doesn’t change anything for me.”

Suppose now you give me the data.  My opinion surely shouldn’t change – it’s just some data set producing the statistician’s opinion, as I knew it must be.  There’s no way it could be especially convincing relative to other possible such data sets, not if the statistician and I started out with the same prior about the drug’s effectiveness.  So now the statistician and I disagree, even though we know the same information?

What is now the difference between “me” and “the statistician”?  If you put the “me” from this example in the statistician’s place, can “I” reach the right conclusion?  How?  (I haven’t read all of the posts on this problem, so someone may have already answered this.)