The article presents that caveat straightforwardly:

   The popular view of America's upper class is that of an
   ossified aristocracy. But research from the National
   Bureau of Economic Research shakes up this view, at
   least among America's richest individuals. 

And elaborates:

    Over the last 30 years, income inequality has grown and
    intergenerational mobility has decreased. The rich are
    getting richer and drawing up the ladder to the upper
    class with them. 

    The story differs for the members of the Forbes 400 List.

So I'd say you're in violent agreement with the author.