Completely true.
Piglet was supposed to be Fleur's version of Martha, Tanya Burr's city, instaworthy dachshund. Dachshunds are hunting dogs, quite stubborn by nature and require training. Martha lived in city since she was a puppy, so she got used to it. Piglet never did, I remember how Fleur used to force her to drive around in a car, but she was so scared. Other than that, I have never seen her try to work with her dogs. I don't know why she then complains about a hunting dog, running away into woods. That is their instinct, which you never worked with, cause you wanted a purse dog.