The article states "The excess educational investment [...] that children born into a typical one percenter household receive is equivalent, economically, to a traditional inheritance of between 5 and 10 million dollars per child": it _does_ cost money to provide this kind of environment. This is why the 1% gives birth to the next 1%, not because they're better than the rest (again, according to the article).
Disclaimer: I may have to plead "guilty as charged" here, if I'm allowed the conceit of placing myself in this aristocracy. Educating our children well has been a defining theme of the culture of my family, going back generations.
With that said, however, a strong factor in educating children to join any "ocracy" is wealth. This can't be overlooked. This aristocracy is not only providing education, but also the environment within which kids can receive that education continuously from birth through young adulthood and possibly beyond. This environment is safe, engaging, surrounded by educated and education-loving adults, and free of violence.
Also, I tend to prefer saying something like "valuable work" rather than "hard work." From my vantage point, hard work is something like carrying a hod, working in a call center, or some other kind of physically or emotionally stressful labor. I hope to never do hard work if I can avoid it.