Breeders feel that they are entitled to whatever they want whenever they want, and they instill these same selfish beliefs in their kids. So in spite of signs clearly saying to not pet that particular dog, they did it anyway because they are above the rules like all breeders and brats. I don't know if the kids could read or not, but in any case, Moo should have been watching them and not let them touch the goddamn dog... or any dog, for that matter. It could have been one of those delightful teaching moments parents have have the opportunity to have on a constant basis - she could have taught her kids how that dog was working, how it was different from a regular pet dog and when it's appropriate to pet dogs. NOPE! Help yourselves to random people's animals because the world is your backyard/toilet/toy store!
One day, those kids will pet the wrong animal and they'll wind up needing their faces sewn back on or losing an eye, and it'll be the Moo's fault for not teaching them any boundaries. It's real easy to be a shitty parent when the consequences don't affect the parent themselves. Oh sure, she can scream and bitch to have the offending creature killed, but killing all the dogs in the world won't undo the damage done to her precious dumpling.
Odds are the dog's owner probably didn't want to make a scene or get into it with a Moo because Moos aren't really known for their rational thinking. The vet was probably concerned that everyone would side with the Moo because "they're just kiiiiiiids" and "they just want to pet the doggyyyyy!" Like it won't do any harm.