In those cases the children aren't being properly schooled anywhere ( home or the institution).
It has been my anecdotal observation that all academically successful children are homeschooled or afterschooled. This is true even when the academically successful kid comes from dirt poor and illiterate immigrant families.
Where are the studies that show where learning is happening and who is doing the instructing? You won't be able to find them because these studies have **never** been done. We spent up to $30,000/ child/year in a socialist-entitlement schooling program and NO ONE has ever checked to see if it is effective or not.
Allow me to provide you an example: Me.
My parents were good, decent, honorable people. My dad was lucky to graduate high school; I saw his report cards. My mother was a little more successful academically, but a college education wasn't anywhere in the cards.
About all the afterschooling I got was, "Did you do your homework?" Mind you, my parents appreciated the value of education, especially as their lives turned out to be difficult, at least when my sister and I were young, but they were inequipped and overwhelmed by working to keep the bills paid.
A teacher changed my life. She told me that I had a gift for academics, and that if I studied and worked hard enough, I could achieve things beyond my dreams.
She was right. That's why I entered teaching as a second career. I look for children that I might inspire.