| There are some kids who would be tops no matter where they went to school or if they were homeschooled. In some cases, the right school, the right activities could be the tipping point. But you can just as easily miss as hit.
It is true that if you home school at a very high level, and your child is a great student, you can trump the public schools. You can also avoid the grades and the class ranks, and the recs of the school which can be instrumental in an app that is viable at the top colleges. Without the mundane rigor of a school day, there is a lot of time to do other things to build a phenomonal resume. When you are at school, you tend to want to participate in the school community, socialize with friends, try out some new things, all distraction to the pursuit of excellence in a few limited endeavors. Much of being a normal highschool kid is not considered great stuff to the top colleges. So by cutting that out, it leaves a lot more time to focus on a few activities, which is what colleges want to see. Passion and excellence.
But it isn't that simple. Just because you direct things that way, does not mean you are going to get that passion and excellence. I;ve seen many home schooled kids not quite make the grade on those endeavors. Since you are not participating in a school community, you are going to have to show how you are spending your extra time. So it is the cream of the crop that manages to get into these top schools by performing so well in an EC, as well as showing a high competence level on academics and high test scores.
Home schooling can backfire when you have a kid who does not end up excelling in those areas. They may be the type of kid who needs to learn to be in a group to take courses. It can be a real downer to have to be taught in a class of 20 or more, maybe whay more after years of private tutors and going at your pace. You do take a risk when you home school. Don't even think for an instant that you are a cinch for HPY because you are homeschooling. Does not work that way. | 
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