I don't know if the inverse correlation exists, but I doubt the explanation provided (that smart people often do not know or won't admit what they don't know).
Coming from academic circles, we consider such people as the "mildly" smart. As in, being uninformed is OK (you know you are uninformed). Being only a little informed is dangerous (you don't know what you don't know). And the most informed are OK too (they know quite well the limits of their knowledge). The smart people you are talking about do not usually survive academia.
In my own personal experience, I find the false confidence to be quite orthogonal to intelligence. I see plenty of low intelligence folks have the same problem, and plenty of high intelligence folks have it, and do not see a clear relation where one is more prone to it than the other. More like: You are humble and always doubt yourself (which is the academic's concept of "smart" - continually trying to tear down your own theories), or you are arrogant and do not. Intelligence is unrelated.
Coming from academic circles, we consider such people as the "mildly" smart. As in, being uninformed is OK (you know you are uninformed). Being only a little informed is dangerous (you don't know what you don't know). And the most informed are OK too (they know quite well the limits of their knowledge). The smart people you are talking about do not usually survive academia.
In my own personal experience, I find the false confidence to be quite orthogonal to intelligence. I see plenty of low intelligence folks have the same problem, and plenty of high intelligence folks have it, and do not see a clear relation where one is more prone to it than the other. More like: You are humble and always doubt yourself (which is the academic's concept of "smart" - continually trying to tear down your own theories), or you are arrogant and do not. Intelligence is unrelated.