I've just took arch for a walk, and one of the things because hes so well trained, lots of people want help training their dogs from me. One of these is a kid who i will call becky.
becky has a 8 month old lab pup, and is having some problems with heeling, so we went for a walk and tried to *sort* stuff out. So dylan* is off lead and doing puppy recalls and is pretty reliable when off lead, so we let him off.
next comes 2 people with a staffy (off lead) and 2 little kids who I would say are about 6 and 8. they are running around relativly close to becky pactising puppy recall, so dylan gets a bit distracted and runs up to them, tail wagging to say "hi"barley withing 2 metres the little girl (6) starts crying, screaming and running flapping her hands in the air, so of course we call dylan back, (which he does) and put him on lead. the dad has a go at becky, who shouts "if you cant control your dog, put him on lead" at the same time hes shouting for his staffy who has wondered off somewhere to call after him.
I magnaged to stop myself from going up to him and saying how he could at least teach his kids to behave when around a dog if its bounding over to them and they dont wanna play/scared of them (stand still, tree position(arms crossed ), no eye contact) and teach them not to make sudden movements/noises otherwise he will think its a game. This guy has also owned a rottie thats been poorly outta control and got into the local secodary school, and nearly attacked (very agressive)archie whilst being in control of two young girls about 9.
I personally put summer on a lead as soon as I see children because they are unpredictable and may do the things that that little girl did. No matter how well trained she is like you said, when children run and scream the dog thinks "play!" The only time she is really off lead is on the beach or at the dog park.
I would not be training an 8-month-old Lab pup, especially your first few training sessions, off-leash in an area that is not fenced in. Even if children grow up around dogs, you can not predict how they will behave when an unfamiliar dog runs towards them.