My family home schools our children. It coincidentally helps solve this particular problem. (Perhaps it also reduces the likelihood that we spread viruses like the flu).
Making public education more distributed by the use of technology could certainly help with security.
Even so, this represents, very optimistically, a dozen or two hours of interaction with others a week. It cannot hold a candle to the interaction children going to schools experience.
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.