That's because there are roughly two types of home schoolers, and they're at opposite ends of the achievement spectrum. The high achiever cohort are the ones you see who outperform students in their GPAs, SATs, and get into highly selective colleges. The others don't even finish HS much less apply to college so you don't hear about them.
Sure, I don't contest that. Parents can definitely fail to educate their children properly at home. Students in government schools suffer from the same problem though.
The point is that the average result appears to be better.
My point was that the average result doesn't account for the lowest performers because they're not even included in those scores that are being averaged. It's skewed towards the high performers.