They said the dog doesn't bite?
I think there's proof on Molly that he does! I think you should still go to the vet and have the neighbors pay for the checkup. Also I would call the dog warden or animal control and report that their dog was out loose. They even admitted it happened before. Nothing serious happened to Molly but what if there's a next time? what if they dog hurts or kills another dog? Then you would have said you wish you would have reported it.