Doggy dilemma

I was not sure what to post this in but I wanted some outside opinions. We had my parents watching our dogs this weekend so we could go on a mini vacation. Well when we were gone one of our dogs attacked the neighbors dog. They said the neighbors dog came into my parents yard and thats when she attacked it. My dog is a German Shepherd and is trained to be a guard dog and is good with other dogs but needs to be properly introduced to other dogs first, so I think she thought she was just doing her job. The other dog I believe is a golden retriever mix and was taken to the vet and is going to need surgery that will cost $600. I have already said that I would take care of their bill, but my dad thinks the neighbors should pay because the dog should not have been on my parents property to begin with, and my mom thinks that they (my parents) should pay because it was on their watch. I think my dog, my responsibility and I feel horrible for the other dog and feel its the least I can do. Who do you all think should pay?