What happened? 1986 to 1988 happened, as is evident from the 1970-2006 trend:It helps to know that the 1986 tax reform created big incentives for people who had previously reported income on corporate returns (where it is invisible to the datasets above) to report on individual income tax returns (where it appears as an out-of-the-blue increase). And if this may be considered a permanent change in the tax regime, then the effect is for more income to show up on individual returns after 1986 than before, artificially lifting the top income share in every subsequent year.
As Winship points out, this doesn't mean that US income inequality isn't higher than that in other countries (though it does illustrate how hard it is to calculate). But if the trend isn't very different, than that changes how we explain inequality here. Explanations involving very US-specific factors, like "culture", our tax policy, or some sort of capture whereby the wealthy have somehow rigged the system in their favor, become much less compelling. Rising inequality (and slower income growth) have been a rising trend across most of the developed world for three decades. We need a better explanation than greedier rich people, or stupider politicians.