A couple of stories along these lines...
When I was young, maybe 2-3 yrs old, I proceeded to crawl underneath the kitchen table to take a bone away from our dog. I got the bone and a bite on the nose for good measure. Got a couple of stitches for my trouble...Both parents were in the room, both yelled NO when they saw what I was doing, but I didn't listen (Per usual lol). I learned that day to never do that again. My parents kept the dog, nothing else happened and I learned an important lesson.
Years later, different dog. Our neighbors behind us, their older child was climbing the back yard fence with cookies in his hand. The dog snatched the cookie through the chain link and minorly hurt the kids finger in doing so. Dog was sent to pound for euthanasia. The ONLY reason I can think of for this scenario being different enough to warrent death was the fact that it was somebody else's child that was injured and their parents would have created a stink. But, the pound refused to destroy our dog as she was too nicely behaved to do that to, so my aunt adopted her and she lived out her days with never another incident.
Now, a dog that viciously attacked my daughter 15 years ago for bending down to pick up a ball they had been playing fetch with for 30 min previous with no trouble whatsoever was allowed to stay home for it's quarantine and was never offered nor ordered for destruction.
Yet, since 2005, my own dogs, who have never done anything themselves, are illegal and considered "dangerous".
Almost 40 years of having dealings with dogs and years learning about them for a career, and I have yet to see what would be considered an advancement of education or common sense when it comes to the issue of canines and their owners, let alone any good common sense legislation to deal with these issues.
The mother in the OP should have taken the time to stop the child and improve the situation, but if you look at the pic, the child seems fine with the dog and probably did learn that actions have consequences. Let's hope that the mother learned something as well!