I wouldn't assume that a dog growling at me was trying to communicate friendly feelings, MF. I would think a growling dog would be communicating barking, chomping or chasing feelings.
FWIW, I don't necessarily think that the lady was stupid, but if I had been in Yorkshire's place I'd have been thinking the same thing. Kind of a kneejerk reaction when your small child is face to face with a growling dog which has not been properly restrained.