...I hate to break it to you, but from what I've seen both anecdotally and in the limited studies done on such things, you've got it exactly backwards regarding social skills.
Some employers (Chik-Fil-A was particularly noted for this) have specifically sought out homeschooled young adults, because they were more likely to be respectful to people and socially capable. Funny, how not forcing children into low-supervision, high-social pressure containment structures for 6-7 hours a day for 13 years straight might make a difference in things like that. The particular crux of it is that homeschoolers interacted with adults who expected to be treated with respect, and got to choose who among their peers to interact with or not more often. They were not forced to spend time with people who treated them and others poorly.
Home school is not for everybody. But more often than not, it does better than public schools do; in many cases, if the public schools in the area weren't so terrible, the parents wouldn't have chosen home-schooling.
Also, while I'm sure there are some cases where homeschooling parents practice helicopter parenting, more often I've seen it that such parents are more likely to engage their children in interesting 'risky' activities like river canoeing, archery or rifle practice, camping, hiking, etc.