The way home school advocates tout the superior results of home schooled kids is a little simplistic. The very act of home schooling is a vote of no confidence in public schools. And while public schools may be incompetent, even if they weren't - of course a home schooled kid is likely to perform better. He is being tutored one-on-one.
Even the most strident pro-government school zealots tout smaller classroom size as an advantage. What could be more advantageous than having a classroom consisting of your kitchen table and (maybe) your siblings?
One-on-one instruction is better for most everyone. Just ask anyone who has taken a foreign language class vs. someone who hired a personal instructor. I bet some of those underperforming public school students would see their results improve too if their teachers focused on them alone.