The big difference about that reinvention is that there are way more parents present in those environments than the typical public school variant. So both good behaviors to observe are more visible and also interventions are significantly more frequent.
> To the detriment of public schools, it should be noted.
Yes, but what means of violence do you possess to be able to force these parents to be involved in the education of other people's children?
There's also a variety of kids' ages at these events, so the younger can learn from the older (and parents can easily intervene if this isn't going well). And you know who your kids are interacting with: you know something about the families, or at least know someone who knows them, so the odds of malign influences are much lower.
It takes more effort to homeschool than farming it out to public schools, so you're naturally selecting for involved parents. To the detriment of public schools, it should be noted.
It also skews the perspectives of homeschool parents into thinking "this is the best system, why doesn't everybody do it?" The answer is, of course, to take the good aspects of each system and make the public school system more viable again, but there are too many entrenched interests on both sides for this to be easy.