The bat is probably to keep other dogs from attacking the dog.
I have a giant breed of dog and I carry a dog lead (chain) to defend against other dogs coming over in an aggressive way. I get sick of people saying 'he only wants to play' when in fact the dog is coming at my dog with its hackles raised in an obvious attack! Of course, even though my dog is on a lead, if a fight ensues then my dog will be blamed for injuring (or worse) the other dog, simply because he is a big dog and will come off best.
The owner is unlikely to be carrying the bat to use on his/her own dog.