Saying that there is no relation between income and cognitive skill is very different from saying that there is some fuzziness in the relationship. Cognitive abilities obviously do influence income, but there may be room for other factors to enter into the equation. In fact, that's my understanding of what "unobserved skill" is, after all - something traditional economists can't explain.
I'm an engineer, and lots of people I went to school with are making more money than I am now because they went to business school or law school. It was sort of understood that that's where you get the most money, power and prestige. I considered myself just as capable as those friends of mine, but the profession just isn't as lucrative (not that I'm doing badly, by any means). And I'm doing lots better than the friends I had who went into history or academia in the liberal arts, who were also very capable people.
There are plenty of things which determine your choice as to what profession to enter, like quality of life (for people who choose academia), family considerations and what kind of work you find most interesting/rewarding. These kinds of considerations can't be handled in standard economic analysis, even though they are very real human motivations. Perhaps these effects are minor compared to the lure of cash, but I can imagine that this accounts for some of the "unobserved skill", or otherwise unexplainable factors which account for wage rates.