You know this how? You're still in high school, aren't you?
Their due success is going to come whether their family is rich or not. True, even if they do apply themselves as much as they are able, they might not be relatively successful. However, it's much more likely that they do become so if they actually try.
You did not answer my question: You know this how? The United States has been proven to be one of the most difficult countries to overcome your born-in class designation -- if you grow up poor, you will most likely remain poor for the duration of your life; if you grow up rich, you have a good chance of remaining rich for the rest of your life.
Public schooling is an option while you are young; however college costs money and financial aid can only take you so far. The college that you go to determines your place and line of work. Going to a low-rated, cheap, community college will not earn you a job at a fortune 500 company, but it will earn you a job -- a much lower paid one. This assumption, of course, is assuming that you follow the traditional linear path of life (elementary school -> junior high school -> high school -> college -> work -> family) that many assume everyone follows when most do not. Those without significant financial support are forced to obtain jobs during their early years of life. This, in turn, reduces the amount of time they can spend going to school and generally results in lower grades due to stress and lack of sufficient study time. The need for food, clothes and a home outweighs one's schooling goals, whether they're truly motivated or not. Those who live in low-income neighborhoods are also more exposed to bad influences such as drugs, alcohol, unprotected sex, and school's filled with teachers who truly do not care if someone falls behind (I've seen this occur first- and second-hand at one of the most reputable high schools in my
middle-class district). These factors can further hinder their chances of following the traditional path. Work ethic is not necessarily a determinant factor of success. Your environment plays a significant role in your future.