That article (or rather, the article linked in that article) doesn't contradict your intuition, just a specific interpretation of that intuition. The randomly generated data puts everyone around 50%, which is indeed what you would expect from randomly uniformly generated data. So the similarity that the generated data presents is supposed to imply the conclusion that "everyone thinks they're about average, so their judgement is no better than randomly guessing (assuming that the guesses are uniformly distributed)", which is a subtle difference from "dumb people think they're smart" - the latter attributes some sort of "flawed reasoning" to one's self-judgement, while the former specifically asserts that there is absolutely no relevant self-judgement going on.

edit: You would also be correct that this doesn't disprove the previous explanation, it just offers an alternative explanation for the observed effect. The fact that data matches up with a generated model definitely does not prove that it is not actually caused by something else, which is one of the criticisms of that viewpoint. It is obviously easier to rigorously demonstrate a statistical explanation than a psychological explanation of course, due to the nature of the two different fields.