No, the breed of dog is important too, in this story, the kid was critically injured and there is a type of dog that routinely does this kind of damage, and it ain't Labradors, and it ain't Yorkies.
Most kids grow up with a family dog. My point was, no matter the size of the dog, they need to learn how to play with dogs. I am not following you that a dog that barks at the garbage man and other boundary threats in the life of a dog is a threat to children ~inside~ the boundary who venture towards the fence. Kids and dogs play in back yards every day, and most don't get mauled. Really territorial dogs are a threat to intruding children, yes.
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.
I got my 21 pound spaniel mix from the SPCA when he was about one year old. That was just over three years ago
He generally has a wonderful temperment, but he was and still is scared of children. I don't know for certain why he ended up with the SPCA, but I am willing to bet that he was mis-treated by a child during his first year.
Children can be remarkably cruel.