I'm doing some tagging, thought I'd update...
She ended up doing *zero* camps with friends. She was supposed to do one camp with up to three friends, but all of them ended up not being able to do it. A girl she vaguely knew (same school, same grade, but haven't really crossed paths 'til now) was also in that camp, and they became super-great friends. So that worked out well.
Oh wait, she did do one short (half-day) camp with a couple of friends. That was fun for her, too.
I think the moral is "don't worry about it, she'll be fine either way." Probably avoid signing her up with her clingier friends, but not all of her friends are clingy.
Edit: Re-read, about parents...
Yeah, that's what worried me, I remember now. One of the most insistent parents' daughter IS clingy. They ended up not going to any camps together. I didn't really purposely put a monkeywrench in the gears, but didn't go out of my way to make it work, either.