I'm a bit confused, its your neighbors dog that got ran over? The one that Brandy supposedly attacked?
I hate to be a party pooper but I'm a firm believer that good fences make good neighbors.
We have 6 dogs and live in a rural area. We keep them all within a fenced 1 acre area. My closest neighbor is not far away (less than a mile) who has no dogs. There is another neighbor less than a mile from him who keeps 3-4 dogs but left to run loose. Those dogs are constantly in trouble and they even had to put one down because it bit my neighbors visiting daughter who was out for a walk on the dirt road.
I never hear a peep of complaint about our dogs from the very few neighbors we have.
If you don't want problems with your neighbors, get a fence.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France