I can only speak for my family, but we spend lots of time with other families and children. Church, Boy Scouts, Soccer, etc.
Ask yourself, have you ever been in public and recognized a home schooler because of the way they act?
The inverse is true too, how many socially awkward people do you remember from your public schooling? I sure remember a lot.
From my personal experience, I don't see a relationship between home/public schooling and social relationships.