> I can not conceive of a worse way to teach a kid how to behave in Adult social settings than to throw them into a group of other kids who have just as little experience as they do and then expect the group to "figure it out".
You are aware of teachers, yes?
> Probably because well run homeschooling groups tend to have high parental involvement
Everything I've read shows that putting absolutely all else aside, parental involvement is key to a child's success. So perhaps the reason your by the numbers evidence shows home schooling to be better is simply because it's a self-selecting group of involved parents.
Probably because well run homeschooling groups tend to have high parental involvement which means the child learns how to socialize not from other children but from watching how the adults they are around handle interactions.
[Edited for clarity in some sentences]