A puritan value that might have led them to believe that the devil could take the form of a dog is that they took the bible literally. When the bible states "Thou Shalt not suffer a witch to live" they figured they had to kill anything that was showing a strange sign of being a witch no matter if it was an animal or human being. The puritans probably would have hung dogs because they may have been looked at as accomplices of witchcraft. Meaning if their owners were witches their animal was an agent that carried out their devilish commands. This situation is similar to a relationship with our animals, if you train an animal to do something their going to follow through because it's what your training them.
