In almost all studies I've read this could be completely explained by self selection, either of the parents opting for homeschooling (i.e. the share whose kids were better than average in school still were when homeschooled) or with unequal response rates (i.e. the parents whose kids had problems at home or the home had problems and thus opted the kids out of school didn't return the questionnaires).
This phenomenon is quite common. For example our midwife told us home births have less complications than hospital births. Well yes, because complicated births usually either already start at the hospital or get transferred there once things get messy.
Please elaborate...
WAT.