J, you seemed to have missed my point here. That point is that if you know your dog's behavioral quirks, you take the steps to minimize risk - ie. you find the park that nobody goes to, the beach where your pooch can run free without having to worry about other people/dogs. You go to places where you can minimize the impact of running into OTHER people's dogs who you think may cause problems. For example, at one of our local beaches, there seems to be a high proportion of small dogs/unsocialized dogs (their owners believe them to be too precious to associate with any other dogs)/and various badly behaved dogs. We stopped going there because we know that our dog can be overprotective and doesn't like when OTHER dogs come sprinting toward us or when they are overly sniffy. Frankly, we have other options and people on that beach can have their little encounters. We go to places where other dog owners are smart about how to control their dogs and expect the same from us. BUT, they also seem to realize that sometimes dogs just don't get along...yes, we ask if we can let them both off the leash, or if it's okay to play...but sometimes, dogs just don't click. It's not the owner's fault, or the dog's fault, it just bloody happens. How many other dogs have been apparently friendly when they met your dog and it just went downhill? I can't tell you why it happens, even with dogs our BC has played with before.
Regarding playing with other dogs, if you are doing your own little training thing, that's cool. I'll keep my dog away from it. But some dogs are social, they like to interact with their environment, just like humans. Have you ever just started talking to someone in the check-out line at the grocery store? Feeling a little social? What's the difference? The only difference as I see it is that dogs have a different language to say "bug off." In my experience, people who don't understand dogs think that a little rough play is going to send their precious to the vet. Our dog is an alpha (as are most BCs) and likes to make that clear right away. But we've also seen that a quicker, faster, smarter dog and a few quick barks can make her behave in a submissive manner. From then on, it's happy-happy-joy-joy playing with no further problems. But they have got to have the opportunity to make that relationship clear. Dogs who bark and bark on the leash already feel insecure about being on the leash. Once we got Alka off the leash, she's a whole other dog.
You also seem to have missed the point about playing with children. Our dog doesn't have a problem with children, she just sees them as little humans or possibly two-footed sheep. She has never hurt a kid, and she's spent a lot of time around them. She doesn't nip, herd, etc. But it has taken some time to overcome the desire to just rush over and say hi. We have some tricks that we use to control it. For example, she loves to play ball...when we're on the beach, she's easily distracted with that. I use that to keep her concentrated on me and not the things around us. But I'm not opposed to playing ball with random other dogs. I love dogs, as I'm sure everyone who reads this does. But the difference seems to be that I love all dogs, not just my own. I'm an extrovert, my dog is the same. We like to talk to other dog owners, we like our dog to interact with as many dogs as possible so we can learn about how she will react and what we can do to help her. When kids come up to pet our dog, we use it as an opportunity to see how she'll behave, but we issue fair warnings beforehand...she likes to jump up, so we'll keep her on the leash. If they want to play with her, we try to let them know that she doesn't like when people stand over her. Every interaction is an opportunity to teach our dog, to learn from her behaviour, and to educate other people about how to interact with our dog.