If you want to look at it from a legal sense, then you need to look at who owns the boundary fence? If its yours, then it "could" be that a solicitor (if they persued it) could make a case against you for not securing your property sufficiently, however that would be highly unlikely. It would most likely be down to the neighbour to ensure the safety of their dog, as you have ensured the safety of yours. I asked my neice for you, she is a lawyer, she feels they have no case really and paying the Vets bill will only make them think you feel responsible, which you are not. Perhaps letting the