I attended summer camp as a child and there were many kinds of kids there unlike myself. I also played soccer for 12 years in leagues which had nothing to do with government school. I also belonged to Indian Guides as a child. Although I did attend government school I had many opportunities to interact with other kids outside of school.
You make my point with that all-important qualifier: "... parents can involve their kids." IOW, the parents are controlling their kids' interactions, leaving the kids with little opportunity to deal with situations on their own.
Of course parents should control their childrens' interactions. Who else should control them? And even if parents are over protective, so what? Children will grow up someday and learn to interact on their own and hopefully not to repeat their parents' mistakes.
I'm not saying that parents shouldn't exert some control -- it'd be irresponsible not to. However, parents should not control all of their kids' interactions, because outside of communes and tyrannies real life doesn't work that way. One has to deal with all kinds of people, and it's not something one picks up easily upon leaving home. Kids have to learn to deal with people early on.
In the end, it's a delicate balance of freedom and protection.
Homeschoolers tend to be quite protective in the first place, and need to be careful about overdoing it. I've known several home-schooled kids who have difficulty interacting with others, and they tend to be the ones whose parents are too protective. (I'm admittedly painting with a broad brush here, but I trust you'll see what I'm trying to get at.)
Public schools, like the army, put a lot of disparate people together in the same place, and they have to learn to live together. That's an important and useful lesson -- provided, obviously, that there is discipline to keep the bad actors either in line or out of the picture. (Lack of serious discipline is one failing of many public schools).
And even if parents are over protective, so what? Children will grow up someday and learn to interact on their own and hopefully not to repeat their parents' mistakes.
All too often they end up as ninnies. There's a reason that "momma's boy" is (or was) considered to be an insult.