I think the big question is about how the legal system tries to separate the ability of a human mind to weigh and process information to reach a decision from the collection of facts and evidence presented as part of a trial. The jurors sought are those at the intersection between people with large collections of 'well processed' information and those with no knowledge that could in any way relate to the case.
This is like saying that for a fair peer-review of a synthetic biology paper should be performed by an electrical engineer or a statistician, or a sociology paper reviewed by an ecologist. A solid paper would have to be understandable and deemed correct by such a reviewer with reference to an agreed upon collection of textbooks. Even in these cases the common language of math is often shared, and it must be acknowledged that differences in math comprehension could alter the weighting of a paper (for example, knowledge of stochastic modeling...). If a sociology educated reviewer consulted wikipedia for their knowledge of island biogeography in a review of an ecology paper, they risk contamination of that space in the knowledge landscape previously agreed upon as being virgin. This information, even if recognized as inaccurate or deemed by the reviewer to be unimportant, may inadvertently alter the interpretation of the paper.
I personally think that, just as peer reviews in academia are most efficiently performed by experts in the same field, a jury should be comprised of a collection of experts with diverse opinions and backgrounds, culled only for direct knowledge of the case, bias, and inability to communicate and work towards common understanding or solutions (in other words the ability to adjust their interpretations in light of new data or better fitting models).
However under the current system mistrials based on something like this do make sense. I also agree that the juror should be held responsible for the infraction. If you want access to materials on a topic you should be able to request, for example, a list of paper abstracts or a summary agreed upon by both sides. We need to also remember that the 'information' a jury is required to consider may consist of much incorrect data and many deliberate omissions. reaching a verdict is really a pretty abstract puzzle to solve, and extra or different pieces can lead to new options for solutions, so much of the process is dedicated to controlling variables.