I blame Barbara Woodhouse, remember her? "Walkies!"?
I think she was the first one to really gain attention with the line "no bad dogs".
I understand the motivation, she was famous in the era I came from where rolled up newspapers and "rubbing their nose in it" were common training techniques. Probably not the best for the dog.
Anyway, what appears to have happened in the average dog owner's mind, is that No Bad Dogs implies Dogs can do No Wrong.
Dogs can do No Wrong, means that if the dog does something that appears wrong, than it MUST be the humans' fault.
TADA! Dogs suddenly are a vengeful deities who must be placated, appeased and sacrificed to so that nothing bad happens to their human subjects.
Dog bite you? It's your fault, you must have provoked it!
Dog kills your livestock? You should have put up a better fence!
Dog harasses your animals and you shoot it? You HORRIBLE PERSON! It was just PLAYING! HOW DARE you kill my DOG just to save your worthless animals?
Dog barks all day? He's just trying to protect his owners!
Dog kills your kid? Well, just see the comments after any news article of the sort and you'll see all the nauseating excuses.