The difference is you cared and you did something about the situation. You replaced the chicken, and when you caught your dog killing another one, you let her know that was not acceptable behavior. It doesn't sound like your dog is constantly loose creating a nuisance in the neighborhood and always killing people's animals. Sometimes things do happen, and I think most people understand that as long as you care and try to fix the situation.
For me, the owner's attitude makes all the difference. If you know your dog is always out and do nothing about it, it is definitely your fault when he kills something or bites someone. If he sneaks out the door, that's different. People's house dogs or well cared for outdoor dogs also don't seem to cause nearly as much trouble as those outside dogs that get almost no attention and are bored to death.
It sounds like you handled the situation very responsibly and honorably. Your dog did something bad, but you handled it right. And the chicken flying over the fence was definitely not your fault, lol.
For me, the owner's attitude makes all the difference. If you know your dog is always out and do nothing about it, it is definitely your fault when he kills something or bites someone. If he sneaks out the door, that's different. People's house dogs or well cared for outdoor dogs also don't seem to cause nearly as much trouble as those outside dogs that get almost no attention and are bored to death.
It sounds like you handled the situation very responsibly and honorably. Your dog did something bad, but you handled it right. And the chicken flying over the fence was definitely not your fault, lol.