I'm confused. If there are cognitive taks tasks that aren't correlated with cognitive ability, doesn't that just mean that the conventional definition of cognitive ability is wrong? (Probably insufficiently multidimensional)
Yeah, it's bad wording. "Cognitive ability" generally refers to g. Calling g "cognitive ability" is valid - if a bit confusing - since it more or less correlates with most of the things we would consider cognitive, though as this chart shows, not all. But if you want to be exact, you should say just g and not "cognitive ability".
Here. From this 2010 book chapter by Stanovich, Toplak, and West. (Here is the book.)
See also Baron's table of cognitive biases, the normative models they violate, and their explanations.