I have absolutely no interest in who posted the post I'm jurying, or who they are talking to.
But sometimes the posts are nonsensical without more context from the thread - for example sometimes people hit reply to the wrong post so the response I'm adjudicating isn't actually a response to any of the posts you have included for context. In deed tracing that is called a wild deed, since it isn't related to any existing deed (or in this case, any post quoted in the jury system). In other cases the forum might matter, since there are different rules in different forums - not to mention somewhat different cultures. I've also had times when there were things missing from the post I was jurying - IIRC something about pulling the post into the jury system broke the links, or other times the post was edited while it was in the process of being juried (and, if I recall, the innocent edited version of the post appeared in the jury presentation - with the vile original post still accessible in the post history - but only if you visited it in the thread
My recollection from when the current version of the jury system was introduced is that it was perfectly fine to go to the thread for missing context, because simply using an algorithm to select which posts ought to be relevant was not a perfect way of including the relevant posts. We just couldn't post or otherwise interact with DU until we completed jury service. So the warnings weren't "you don't belong here" as much as they were a reminder that while I was serving on jury duty my ability to interact with DU was limited. So I don't really think it is fair to suggest I'm on a page I have no business being on. If that is the case, it is probably pretty easy to actually revise the software to prohibit it.