A lot of the income inequality/mobility discussion has, as part of its background the fact that most of the really wealthy are "self-made" which, as far as I can tell, means they didn't inherit their great wealth. But there's a problem with that fact: it doesn't count leg-up wealth. Mitt Romney is a good example. Everyone knows he was born to wealth and opportunity, but his current wealth is "self-made". Sure he inherited (or would have, not sure on the timing) lots of $$, but he has made quite a bit more.
Even Bill Gates, who most people see as an innovator and self made man, had pretty well off parents. The children of wealthy people have advantages that others don't, even without looking at some big inheritance/gift. They can afford to take more risks and chances than most people, because if they fail, they won't be destitute. Bush Jr. failed at every enterprise he ever attempted and he was gifted the presidency thanks to daddy's little supreme court justices!
That America has lots of "self-made" extraordinarily wealthy individuals is not a testament to America as a land of extraordinary opportunity unless rich, middle class, and poor alike all have the same chance of making it.