I think this is a very popular argument, because it sounds reasonable on the surface. However, I suspect that it is similar to the pre-Galilaen notion that heavy objects fall faster than light ones; sounds reasonable, but completely untrue.
I touch on statistics in the math I teach, and I did have one class of it in college, but detailed statistics are beyond me. However, it would seem to me that if success were based solely on personal choice (or even primarily) we should be seeing a lot more randomization in our national results. If it was all about choice, we should see fairly even percentages of success or failure regardless of gender, race, or socio-economic status. Though, like in roulette, we may occasionally get "runs"; given 300 million people over decades, we should be seeing a relative balance.
Since this is not what we find, it would seem that there must logically be other system factors that are causing our stratified outcomes. Now obviously, those on the higher strata of these outcomes would love to take personal credit for their outcome.... and they would also like to see that that the system factors stay JUST as they are. To justify their position that it is all about personal choice, the advantaged often find some example of an individual who started at the bottom and ended up at the top - if that person can do it, anyone can.
Of course, to use that approach, one would have to violate a basic rule of statistics. In statistics you have items called outliers. These are items that are so different from the norm, that if you include them, it ends up misrepresenting your data set. In the case of the "bottom to top" individual, they are not only including the outlier... they are basing their argument on it. It would be like assuming that because Einstein could do certain equations, anybody could. The truth is, that person who rose from the bottom to the top was a genius when it came to system-defying. Though fortunate for that individual, it would be a mistake to base our policies on an outlier.
There is probably a mathematician in the audience who is going to spotlight all the holes in my logic, but it was how my mind was working on the issue. :)