Considering half the home schooled kids are kept for indoctrination and/or abuse purposes, I doubt it.
Considering they won’t even hold kids back a grade here anymore, I could see it. But I wouldn’t be surprised if the curve of home schooled kid intelligence has two peaks, one corresponding to parents who make their best effort and another corresponding to the ones you’re talking about.
Yup
Homeschooling: A comprehensive survey of the research, Robert Kunzman, Milton Gaither Other Education-the journal of educational alternatives 2 (1), 4-59, 2013
"A final consistent finding in the literature on academic achievement is that parental background matters very much in homeschooler achievement. Belfield (2005) found greater variance in SAT scores by family background among homeschoolers than among institutionally-schooled students. Boulter’s (1999) longitudinal sample of 110 students whose parents averaged only 13 years of education found a consistent pattern of gradual decline in achievement scores the longer a child remained homeschooled, a result she attributed to the relatively low levels of parent education in her sample. Medlin’s (1994) study of 36 homeschoolers found a significant relationship between mother’s educational level and child’s achievement score. Kunzman’s (2009a) qualitative study of several Christian homeschooling families found dramatic differences in instructional quality correlated with parent educational background. "
There’s another bias in that kids with educated parents in public school will also have higher grades on average than the average public school kid. I don’t know how much that might affect conclusions. It doesn’t seem necessary to make the point.
I have no doubt that a private tutor can outperform a public school, but it takes a number of factors, and it’s more difficult to outperform public school combined with that same personal, educated tutor.