I'm on both sides of this. DC have always been taught from a very young age that they don't approach any dog without my (not the owners although obviously I would seek the owners permission) permission. Even then they are allowed to do so quietly and gently. They are not allowed to touch without allowing the dog to see and smell them first. I've taught them how to speak near a dog.
Rarely do I give permission...frankly I don't know that dog so even if an owner says they are fine I tend to make an excuse. Generally I keep them the other side of me and we simply wave hello.
We also have a dog , she is unbelievably gentle and quiet however I still am extremely careful both if others approach and with my own DC who have had it drilled into them how they treat an animal.
It's my responsibility both ways and if there was a chance that my dog could snap that's on me as the owner. Frankly if your dog is at risk of reacting you shouldn't be taking him / her anywhere near where there are children because ultimately both sides are unpredictable.
My dog has had a interesting history and because of that I cannot always be sure. She doesn't bark, follows commands , and is ridiculously gentle and loving...but she is a dog.
Same way my DC are and have been very carefully taught ...but again they are children so they can be unpredictable (3 year old particularly) so as the adult and the owner it is entirely my responsibility to manage it all.
That includes keeping the dog under control and my DC near mine and other dogs.
Basically yes children should be taught to be responsible but ultimately you are in control of the animal.