You cannot help luck (p) but you can help the number of times you put yourself in a position to be lucky (n). The expected value is n x p, so you clearly have a big influence in your success.
For example, going to Princeton gives you a much bigger chance to be seated next to an important Lehman person, and having the right parents gives you a much higher chance to go to Princeton. Some people have such high "n" they are bound to end up "lucky".
I feel compelled to both upvote and comment on your post, in order to further emphasize the point you are making: you can help the number of times you put yourself in a position to be lucky. This understanding is incredibly important and relevant to every aspect of one's life, however diverse, from business to dating. Check out Luck Surface Area [0], a relevant concept largely based on the above.
Also, most often than not, merely beating inertia and getting to do things, no matter how involved or not they are, can have a tremendous impact on one's success. Simple things really work. You just have to do stuff. Other times you just have to ask. You'd be surprised how often you get exactly what you ask for without being manipulative. Rejection Therapy [1] is a true eye opener, especially when the rejection never comes. The way I see it, it's the most profound realization that at that point luck was just made out of thin air.
And while some things definitely cannot change, like the country one was born in and the socioeconomic status of their parents, there are many, many others that can be hacked.
While what you say may (or may not) be right, you have completely missed the point of the speech and its lesson by focusing on the question of how to become successful. The point is, if you do happen to become successful, don't think you deserve it, and don't forget to repay your debt to those who aren't so successful.
This is not a lesson in self-help, but one about one's place in society.
I think you may be contradicting yourself. Using your example, one thing leads to another but it all hinges on an initial lucky roll of the dice: born in the US to the right parents. No one "earns" this head start but almost everyone reading this discussion has it.
Like you, I believe that I've had some say in getting to where I am today, but it's hard to tell how much of that is reality and how much is self-aggrandizement.
Perhaps the way to think of this is by going to Princeton, you increase the chances of sitting next to someone from Lehman. So you're not putting yourself in a position to be lucky, you're reducing your need for it.
In other words, we view the odds of an unlikely event as lucky (the chance you'll sit next to someone important) but the odds of a likely (sitting next to someone who can't get you a job) event as the norm.
For example, going to Princeton gives you a much bigger chance to be seated next to an important Lehman person, and having the right parents gives you a much higher chance to go to Princeton. Some people have such high "n" they are bound to end up "lucky".