Most zillionaires do come from at least solidly middle class backgrounds. I'm sure there's a counterexample somewhere, but people don't go from the ghetto to the Fortune 500.
This is an important point. Most Americans (at least, in the past...) have made somewhat more over the course of their lives than their parents did, but the correlation between a person's economic status and that of their parents is actually fairly strong.
It is almost absolute. It is absurd to state that 'most rich people came from at least solidly middle class backgrounds' -
nearly all of them came from wealthy, highly privileged backgrounds.