Rather, his supposition is that middle-income workers in the US have missed out on gains that have instead gone to upper-income workers in the US. That's false, for the same reason that workers in a single company don't "miss out" on the money given to its executives. As defined by skill sets, the labor pools for upper-income workers and lower-income workers don't intersect, globally or otherwise.
This matters because it affects the solutions we choose. Income inequality is a symptom of the deeper problem of reduced American competitiveness 1) relative to our peers, 2) in the middle- and lower-income labor markets. Because so many more middle- and lower-income skill workers have come online, who are delighted to accept lower wages than US workers because it's an order-of-magnitude improvement over what they had before, these US workers would lose ground merely by remaining as productive as they were 34 years ago.
So in order to maintain the globally-superior wages we have become accustomed to, we must maintain and even increase our productivity edge. How do we do that?
That is the challenge, not income inequality itself. "Fixing" the problem by calling the situation "unfair" (and taxing upper-income US workers out of vengeance for their presumed unfairness and exploitation) isn't a fix at all. It's like prescribing painkillers when someone has a broken leg; the problem isn't the pain, it's the broken leg.