Yeahhhh, definitely not quite. Good education + tutoring + a willingness to work hard can more or less guarantee you'll get into at least one "well respected" school, but if you just sit down and pick one of Harvard, Stanford, MIT, etc., the odds are still very long.

From personal experience, I had all the advantages of affluence (nowhere near the level of these people, but still enough for a good private school and test tutoring) and I worked very hard, and I even had legacy at Stanford--still got a fuckload of rejections, Stanford included.