There's something fundamentally wonky about this whole discussion.

The claim is that people who are bad at cognitive task A are also almost always bad at meta-cognitive task A', which is evaluating their competency at task A. The argument is by turns tautological (people with bad grammar are poor at evaluating the quality of their grammar) and empirical (poor performers who are presented with evidence of their incompetence fail to adjust their estimates of their competence.)

Here is the study that has not been carried out, though (so far as I know): test the same people on tasks that they are good at and tasks that they are not good at. If the effect is universal and explanatory in an interesting way you'd expect people to behave very differently depending on the task, because not everyone is good at everything.

I'm a very good poet (http://www.siduri.net/cindylooyou/index.html, http://www.tjradcliffe.com/?p=58, https://greenteadoodles.wordpress.com/2013/11/24/painting-th...)

I write decent prose (http://www.siduri.net/songsofalbion/songs_of_albion.html, http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/...).

I can't really paint at all (thankfully no examples of my work in this field are on line).

And from my own perspective, at least, I'm capable of evaluating all my capabilities in those areas pretty well. It is implausible that the critical skills that let me evaluate the quality of my poetry--which evaluation is based in part on some very positive responses from other poets, as well as some nice comments from ordinary readers and my own internal judgement--somehow magically fail when I evaluate the quality of my prose or painting. Or vice versa.

The Dunning-Kruger argument depends on the claim that critical evaluation skills are linked to the skill being evaluated, and yet there is an argument that is at least as strong that critical evaluation of performance is a skill that is more-or-less orthogonal to others. I knew I kinda sucked at spelling long before there were universal spell-checkers, because people I trusted told me I did whenever I failed to carefully, manually, spell-check things. I didn't have to have spelling skills to make that evaluation. I simply had to be a mentally competent person with friends and co-workers I trusted, and know how to use a dictionary.

The experimental data they have seem to be basically OK, but the experimental setup may radically limit the relevance of those data to the real world. Poor generalizability has been an ongoing problem for psychological research: very often effects that are seen in the lab don't have any particular implications for the world outside the lab, despite our eagerness to tell just-so stories about them. For example, people who play FPS video games have scores on aggression measures that are statistically higher than those who don't, in the immediate aftermath, but show no greater propensity for actual violence in the real world.

So while I'm not questioning the ability of the instruments they are using to generate the data they are seeing, I am questioning their interpretation of it as it applies to interesting real-world situations, given that it would seem to imply that I'm a mediocre poet and a good painter, and that is simply not correct, unless the poets who praise my poetry are all figments of my imagination, and an extremely competent artist who has seen my painting and said (correctly) it looks like I have no clue what I'm doing is crazy or lying, which is not very plausible at all.