I can't imagine surviving at a top-ten school without having a focused research vision from the start. I'm not saying you should walk in hoping to prove P != NP, but who wants to dedicate 5+ years of their life to working on someone else's research project? Not to mention that these are typically the best years of your life.
I think the real key is to aim for a the top of a hill, not a cliff. You need to pick a goal that enables you to make gradual progress. If you start out by saying "I plan to build the best race car in the world"-- that's fine. Your first paper may be on improving the tires, then a follow-up with an even better tire material, then you discover that square tires can be used instead of round ones (thereby disrupting the entire field of tireology), and before you know it you have a PhD. You never reached the top of the hill like you expected, but you kept climbing.
Disclaimer: I don't have a PhD (yet). :)
Life is an ongoing "learning experience". What you learned in the past allows you to function at a higher level now; and it allows you to learn more so you can function and learn at an even higher level tomorrow; and so on, "forever and ever" (with a little bit of luck).