I don't want to get into a discussion about the numerous merits of homeschooling, but Spelling Bee winners must study the words on their own, regardless of what kind of school they attend. It helps if the contestants read a lot of books, have parents and friends who care about education, and perhaps study more languages, history, and science. Otherwise, studying for Spelling Bees has little to do with the quality of education (or lack therof) in private vs. public schools. If Sai Gunturi had attended a public school, he would still need to apply himself outside of class to learn the words; I wouldn't give his private school the credit for his own determination and hard work.
A couple of years ago, a local public school kid won it. His younger, also public-schooled, brother won the state bee this year, and I believe he competed at nationals.
Let's not let our enthusiasms get the best of us.... ;-)