Just because you don't own a Rottweiler, German Shepherd, Mastiff, Doberman Pincher, or Pit Bull doesn't mean you should let your toddler or small child run around the back yard with a dog double his/her weight.
As a mother, I'd always err on the side of caution. If you have a big dog, let them outside to play. Then, let your toddler outside to play, and put your dog in.
You made a very specific point about dogs being protective of their fenceline and that kids should never be in a fenced area or go near their own fence in their own yard. That's the point I differed on. If you've had that experience, that was a really strange dog.
I didn't say kids should be unsupervised with a romping large dog. I know they can be knocked over. Little kids and dogs should always be supervised, and kids not allowed to play active games unless and until they are old enough, stable enough, and the dog is gentle enough.
I'm glad you closely watch your kids and your dogs. Especially if they may or may not be part pit ;~D
I don't have kids, only large dogs at the moment, and they are required to behave just a little better than the kids who visit ;~D