Here, I use penetrating in the most general sense: of being able to get into a paper, research paper, or study and make sense of it. For classes in many fields I've been required to read. To put things more accurately, there was required reading. I know for a fact that a tremendous number of students don't do it, and although it is required per se, I know many faculty assume (rightfully) that students will not. That being said, they feed into the problem by providing summaries during lecture, and administering exams which ultimately do not require knowledge gleaned from the 'required reading.' In my politics of Mexico course (which is pretty interesting and fairly well taught, regardless), I noticed that the course text, a Cambridge published academic overview of the modern Mexican economy was really not required at all for the midterm. Sure, it made the history portion of the exam extremely easy having read it, but even the TA noted that "the professor surely can't have expected you to read all of it" despite it being a rather minimal 30 to 40 pages over five weeks.
This sort of writing isn't hard to read. Anyone could read it and get lots of information out of it. It was certainly dense, and fairly full of footnotes, but anyone with a lower division economics education could make sense of it. It might take reading through slowly and rigorously but it's not a technically difficult work. It should be thoroughly within the bounds of any student who is enrolled in the class.
Another course I took which featured relatively easy readings was a lower division cognitive science course. This course required us to read papers, but given that the purpose of the course was generally to inform us the structure of most psychology papers and explain the various commonly used statistical tests, it was far from difficult.
In my personal time I've also read research papers by several political economists and political scientists. (including for the blog post I wrote yesterday) Most of these are pretty accessible, provided you have time, a basic understanding of the field, and the willingness to follow footnotes. Also, being on a university internet connection with journal access is tremendously useful, but not requisite. It does surprise me that more people don't check this research when dealing with political or social claims that are made, but frankly all of society at this time probably has a bit of an anti-intellectual bent. Sure, pseudo-intellectualism (this blog!) is all the rage, but in terms of actually reading the relevant works in academia, things aren't super popular.
Now the fields where arguably public knowledge is the weakest is in the sciences. Perhaps this is because it's really hard to condense scientific research in a way which is accessible to the common person. When it's done in the media well it's impressive, but oftentimes it's done poorly and justifiably panned. I was reading studies on GMOs for an arbcom case to see if there was misuse of sources, and frankly, although I was able to make sense of them, it required a lot of googling and time, as well as a reasonable existing knowledge of biology and chemistry to make any sense of. It's easy to distrust writing that says GMOs are safe, when the average person has no opportunity of penetrating the key meta studies. Furthermore, it's hard for the layperson to distinguish in quality between meta studies. (oftentimes the poor ones are pretty good at obfuscating this fact!)
Strangely enough, in one of the fields which I know fairly well, computer science, I find the papers in some subfields to make absolutely no sense. Although ones in things like usability, interface, and document markup make some sense to me, it requires a ton of specialized knowledge to be able to parse a paper on say programming languages or microchip design. Half the time I have no idea what the titles mean, despite having a far-above-average knowledge of both. (Especially programming languages.)
Ultimately, this may indicate the pay gap between the sciences and other fields. Whereas any reasonably educated person can read much of the poli sci research coming out, they are liable to be unable to read the newest technical research. I do grant that the truly great thinkers in poli sci and related fields bring tremendous expertise and breadth of knowledge. They are also able to apply their thinking to a wide variety of issues with high impact. Nonetheless, the impermeability of science research isn't pointless, but it probably contributes to poor public knowledge and higher pay for academics.