So my daughter completed multi-variable calculus at a local university at age 13 and got the top score in the class, sitting along side all the freshman engineering students. She took the AP Bio at age 10 and scored a 5. She herself feels the local schools would not serve her well, concluding this after taking with age-peer friends at gymnastics practice, track club, and orchestra, just three of the activities that provide social interaction for our daughter. You and all your nanny-state know-it-all kindred need to stop telling other people how to raise their kids.
Your nephews, perhaps, are not getting the kind of social experiences that you think they should -- and you may have a point, they may not be served well by their current social experiences. First of all, don't paint all homeschoolers with the same brush. Secondly, is there a permanent harm? Thirdly, you'll never convince me that the socialization of a typical public school with all of it's dysfunctional cliques, dysfunctional fashions, and bullying is somehow better. I can only imagine the kind of severe bullying that my daughter would have to endure at the typical high school, just because she is a girl that likes math and science. Go read "They Sibling Society" by Robert Blye and then try to tell me the current public school system is good for kids' socialization.
I really get tired of people who haven't thought deeply about the problem, haven't read widely about the issues, and don't face the problem in their own life somehow thinking they should be able to dictate to me.