I think the most accurate answer is, "it varies."
My son actually goes to an excellent public school, that works hard against bullying / for acceptance, offers peer to peer counseling training, and more. But that he has learned social skills there has more to do with (a) being a part of the special ed lunch bunch and (b) going to after-care with an amazing care provider, than being in a school setting. It is one thing to be forced into dealing with people daily; it is another to do so effectively, and teachers honestly don't have the time to sit down and break down every conflict to help the child know how to do it better. Which is definitely something AS children need - my son's ideas for improving things tended to be so far off base it was almost humorous. AS kids need it broken down for them. I did that with my son, his resource teachers did that, and the daycare provider did that. If we had not, the forced socialization would have created frustration and withdrawal, not effective learning.
A parent can NOT send their child to public school and wash their hands of having to teach social skills. Yet, some think they can. Even with the best of schools, that just isn't true.
At least homeschool parents start out of the gate knowing that they will need to provide social skill opportunities to their children. How successful they will be varies by the motivation and ability of the parent, as well as what is available in the area.
I would never tell another parent that you MUST do "a" so that your child will acquire social skills, simply because there is no "a" that provides a universal answer. The important thing is for parents to understand their children may need help, to listen to their children, and work out WITH THEM a method of learning that will be effective for the unique individual.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).