Adversity breeding success

A common theme often repeated by many is that "a kid who grows up in poverty and hardship will tend to be more successful". Though this theme does sound inspiring, is it true?

Firstly, let us look at the richest billionaires of the world.

Bill Gates - came from a upper-middle class family (had money to send him to Harvard too).
Warren Buffet - came from a middle class family.
Carlos Slim - dad already had a successful family business.
Li Ka Shing - actually had a rich uncle whom he worked for.
Mark Zuckerberg - see Bill Gates.

We can clearly see that many of them did not really rise from suffocating poverty.

Secondly, if we look at statistics, we can see that people have a tendency to stick in their own class, i.e. kids of poor people tend to stay poor, while kids of rich people tend to stay rich. Of course, one can work to better oneself in life, but statistically speaking, many do not. Even in the United States, widely touted as the land of opportunity, only 3 to 6 percent of families go from poor to rich or vice versa.

Of course one may say that there are exceptions to this, which I do not deny at all. Nevertheless, the statement "a kid who grows up in poverty and hardship will tend to be more successful" is a generalization, thus it can only be defended by statistical evidence, which clearly do not favor it. The truth is that given two kids picked at random, the one from a middle or upper class family is much more likely to be financially successful than the one from a poor family.

I feel that the constant repetition of this statement may damage society by making us focus less on welfare and educational opportunities for the poor, thus I am loathe to repeat it.