The invisible fence will not keep anything from getting into Peaches yard. (Like a child who might step onto the grass). And the current on the electric fence is adjustable. Meaning the amount of shock that Peaches gets when she crosses the line depends on whatever setting her owners have set it at. I'm not a big fan of electric fences (I don't like the idea of shocking an animal to train it) and if that's what these people have to resort to, to have a dog where they live, then maybe they shouldn't have one, or they should move, or train the dog to live indoors and take it out for walks like others in your neighborhood must do!! You're supposed to work with the dog to determine how much of a shock it takes to get the dog to not go past the fence line. After a while, supposedly, you can reduce the amount of shock. But I've heard all kinds of stories of dogs just running right thru it and ignoring the shock, and one guy even told me his dog kinda liked it (the shock was set on minimum) and would actually sit by the line to feel the buzz!!
I'm not a lawyer, just a pet owner, and know how upset I'd be if this happened to my dog. But my thoughts go a few ways on this. Although I'd probably feel that I'd want them to pay ALL of the vet bills, part of me would be glad that they even offered to pay half. Some people wouldn't. If you try to fight it to get more you may end up with nothing only because your dogs did step into their yard. I don't know if Peaches owners homeowners insurance will cover it or not. That part might be worth checking out. But it might come down to considering whether you want to get into a legal battle over this, or settle for them paying half the bill.
If you have a homeowners association are there any rules or regulations about leaving a dog tied up outside that these people might be violating?? I don't know why people have animals only to tie them up. If I didn't have a fenced-in yard, my dogs would be in the house, or on a leash when out.
If Peaches owners are considering her future maybe they will do something about the situation so nothing similar happens to anyone else in your neighborhood.