Unless the dog owner is a lawyer, I wouldn't go by what he said. He may have given you some misinformation to avoid you taking him to court.
I'm not a lawyer, but speaking directly to your insurance company and/or a lawyer about this would be the smartest move for you. Dog bite and premises liability laws can get tricky. Also, each state has their own policies on how animal bites are handled. Contacting both your insurer and a lawyer could give you a clear answer.
This link might help clarify insurance requirements for dog owners: (removed)
This link discusses what dog owners must cover if their found liable for someone's dog bite injuries: (removed)