While the pop-culture notion of the Dunning-Kruger Effect is "idiots don't know they're idiots," the actual results of the paper were (essentially) that F students thought they were D students, whereas the A students thought they were B students. The argument here seems to be that the original effect is explained as essentially a kind of reversion of the mean argument (people assume themselves to be more average than they are), but I don't entirely buy that--especially since the simulation results they present don't really look like the original Dunning-Kruger results, since the crossover point is in the wrong place, and that's actually kind of significant in the original analysis...
Indeed. The true irony behind the Dunning Kruger Effect is that the pop culture understanding of it is essentially describing itself. Showing overconfidence in areas that you have little clue about.