What's their definition of "millionaire"? Thanks to inflation it is now possible to become one just by virtue of having a household of two white collar workers, each making 150k annually, no kids, no cars - after a decade or two you cross 1M USD net worth.
I think it is helpful to define "millionaire" in 1920s dollars ($20M today)
It's been a long time since I've read the book, but I remember the average millionaire household they surveyed only having a single income of $70k or something.
It doesn't surprise me that there can be a lot of movement among the lower to upper middle class brackets. I suspect where the unfairness is really apparent is the bottom 20% or so. What are expected adulthood earnings for kids that grow up below the poverty line?
Once you restrict your stats to those that stay in school and don't do drugs, I'd think it is hard to correct for other causes. Like the presence of involved parents.