...states have different homeschooling laws -- some are as "minimal" as telling the local school that you've decided to homeschool and then never having contact with them again, other states require teaching parents to hold high school diplomas or teaching certificates, some ask that you enroll in an "umbrella" group. We HS in one of the most restrictive states and are required to sign (notarized) yearly affidavits, plus send the district a list of objectives, end of year portfolios, an evaluation by a certified teacher, and results of standardized testing in 3rd, 5th and 8th grades. Studies have shown no difference between the most and least restrictive states in terms of standardized test performance (testing homeschooled children)
However, no amount of district (or local government) oversight will prevent what you describe. Parents who homeschool are (for the most part) making a sacrifice and are truly dedicated to "teaching" (learning with) their kids, but there will always be a few stinkers. This is not a homeschooling failure, it is a parenting failure. Unfortunately, these are the ones that teachers love to publicize...which explains the resentment you see here.
As for the "socialization" (Ick--hate that word) problems you describe...I do agree that schools are more like "Lord of the Flies" than the "sensitive utopia of diversity and understanding" that we are led to believe...these kids are probably wise to be afraid of the other kids (some homeschooled kids may have been removed because of previously abusive school situations)
I am a bit dismayed to hear that you have lost hope that these kids will progress beyond 6th grade level--don't count them down and out yet -- I have seen children make great leaps once they are taught in a way that works for their style of learning -- keep trying !