I don't understand this part. "Completely uncorrelated data" is usually taken to represent the null hypothesis, but that's not the case here. In the DK paper, the implicit null hypothesis is "people of all skill levels are good at estimating their performance". In this case the "completely uncorrelated data" matches an alternative hypothesis, "people's skills have nothing to do with their ability to estimate their performance in tasks testing that skill". This hypothesis doesn't outright contradict the DK proposed hypothesis (and is certainly not the DK null hypothesis), so getting similar results is unsurprising to me, and I'm not sure that we learn from it anything about the DK results.
As for the other study cited, the figure shown in the article doesn't give a lot of information on density, and looking at the paper itself, figure 4 does actually seem to show that self-assessment gradually shifts left with increasing level of education.
(Edited for accuracy).