On the other side of the issue..
I'm on the other side of what most of you are posting.
I've seen invisible fences work well, when turned up enough, and when dogs had the right training.
As far as liability goes, it's OP's responsibility to keep his dogs in, not other animals out. However cruel you think this statement may be, if wolfie comes in and chomps on OP's dog, that's OP's problem. No liability there to rest on the shoulders of anyone but OP.
By OP using the invisible fence to keep his doggies in, OP is doing his duty, no matter how much some of you may disagree with the methods or executions.
Neighbor's visitors, however, allowed their precious little doggies to run around, unleashed, and whoops!- they (assumably) got chomped by OP's dog as a result of visiting neighbor's negligence.
OP is not legally responsible for bills incurred by owners who allowed THEIR dogs to run amuck. To keep the peace with the neighbors, OP could offer to throw in half, but he's not legally responsible to... nor do I really think neighbor's family deserves it, since they think so little of their own dogs safety to begin with.