Again, not in my reading. In the random data thought experiment, everybody (experts and unskilled alike) suffer from the burden of not having the skill to estimate their performance. The author is even surprised that the DK effect in the random data is bigger than observed in the DK experiment ("In fact, as Figure 9 shows, our effect is even bigger than the original") - but that's because in reality, people do have some ability to estimate their own skill. So the claim that the lack of skill is related to the lack of ability to self-evaluate does make sense, or at least, isn't contradicted by the experiment.