Hard question. :( I'm not a helicopter mom, but a present mom. I don't hover over every single conversation and every move my 5 year old makes, but hovering over someone and being PRESENT for someone is different in my opinion! My 5 year old: I go to the playground with him, I play with him sometimes but by this point he is PERFECTLY happy to play without me, run around like a little boy should, having fun. He is great at playing with his little brother (age 2) if there's not other kids his age to play with. (If he has peers there, I play with little guy so he can be big and do his own thing without having to babysit). But I'm PRESENT. I'm there.
Sometimes, I slow down so he can move up ahead, or engage in a conversation with another mom, but I am actually being VERY involved in parenting. I'm watching him, when he thinks he's got an opportunity to act without me on him, because I want to see how he plays with other children: How well does he make friends? Does he play nicely, share, not say mean things? Is he being played with nicely and not bullied? What kinds of things make him light up, and what things make him seem unsure? How does he respond to different things? I'm WATCHING. All the time. I'm learning my son, and I'm learning things we need to work on together at home. But I'm there. But I know loads of moms could be thinking "What's wrong with that woman, why isn't she playing and engaging her child, she's so lazy just talking to her friend or reading that book". But they don't know what we do at home or how engaging I am, they don't know what I'm doing there or why. They're wrong, plain and simple.
That said, accidents will happen. Climbing a tree is not a bad thing, it is a wonderful thing and more children should do it. I was in kindergarten and my backyard magnolia was my sanctuary....later in 2nd grade, it was my "secret" reading spot. When my brother was in 4th grade, he was stronger than me, he could climb better than me, but he still slipped and broke his arm in 3 places. That doesn't make climbing a tree bad, or my mom bad for allowing it. Accidents DO happen, even to good people with good parents doing good things. But I won't take that and hold my children back from being kids. (And for the record, I was showing off on the monkey bars THIS PAST A. and I slipped....I'm heavier than I remember, not as strong for my weight as I used to be, and....I swear it was just a little wet, lol. I landed so hard there was a cloud of dust....I had dust in my mouth AND in my pants, lol. It hurt. A lot. All I could do was just lay there and laugh, but a couple weeks later, I had to go to the doctor for a shot to help my bicep injury. Go figure. And I AM the parent.
I can see my son being somewhere around 8 or 10 and playing at a playground if it were CLOSE, if he had friends with him. (Approximately-I don't think you can just name an age where it's appropriate to do things, because there's nothing magical about an age; it depends on the individual child, and his level of independence, maturity, level of common sense, ability to follow some rules, where he's playing at and with who, etc, etc) But I would need to be outside and nearby. By around 8, I think he'd be able to read any signs of trouble, follow safety rules, keep up with his friends, and phone me or get his bike and come home if his friends were acting up. I'd have him phone me BEFORE he left the park, or if he needed anything at all. My mom was good at being "the bad guy" for me when I felt uncomfortable about something, and I would do that for him if he wanted (or needed) me to. But 6 is quite young to have no parent around at all, but then that's hard to say definitively because I don't have a playground very close to my house at the moment. Our nearest playground is 1 mile away, and that's too far for my comfort zone, for my 5 year old to be alone.
As for Jo W......hmmm.......for the record, I'd like it known that I would really want an adult to get my phone number from my child and call me, and if that isn't possible than call 911 and we'll figure it out later, but if my child is writhing on the ground with obvious broken bones, we need to get him some help please! I think it was perfect that a child nearby was able to run get the parents for help while your husband stayed with the hurt child. Stranger or not, that is most certainly not over the top intervention: running to a hurt and crying 6 year old, calming him, sitting with him while help is coming.....those are the humane responses and I would think very, very ill of someone who didn't try to help in some way.