You can quote all the studies you want, but speaking as someone who was ACTUALLY home-schooled from 6th through 12th grade, I can tell you that whatever efforts the parents make simply can't compare to being in a school for 8 hours a day.
I can of course only speak to my experience, but let me tell you my social skills suffered dramatically because of being home-schooled. Through those 6 or so years I was frequently lonely and had perhaps one or two friends throughout all my time there, whom I would see once a month when my mom took me to the school's teacher, who would evaluate my work and my education. My parents made some effort to help - I was on a baseball team throughout my time at home, but it was glaringly obvious how immature I was compared to others my age and so I made few friends.
Now, about those visits to the district education office (required in Riverside County at least); I looked forward to these less and less because most of the kids there were worse off than I was; shut-ins who didn't know how to talk, or attention-deprived obnoxious kids, and, call it a stereotype if you will, but there were plenty of crazy "fundie" parents keeping their kids out of the public schools whom I actually met. In one very poignant case I remember, the mom stepped in and refused to allow her son to read "Beowulf" because it contained "demonic ideas."
Of course, not all the parents were like that. But the kids more adapted to the environment would simply get away with not doing their work - usually by copying out of the solutions (we graded our own work - there would be spot-checking by the teacher but it was easy to get away with small inflations of one's grade).
I regret every year I spent in the program. When I got into college I was naieve, socially-shell-shocked and had trouble adapting. Perhaps it just wasn't for me, but in my opinion the majority of kids taken out of the schools learn less about life than necessary.