I have to agree. You cannot separate the statistical analysis from the meaning of the study. In the article, the author's random data is exactly an extreme replication of Dunning-Kruger. Why? Because, in his random data, people with low test scores almost always overestimate their ability, while people with high test scores almost always underestimate.

That is precisely the premise of the Dunning-Kruger effect. The fact that the original Dunning-Kruger paper shows a less extreme effect? That just shows that people are slightly better than random at estimating their own abilities - but still nowhere accurate.