Interesting, sorry to hear about your dogs. I will be more careful. I have used that exact material to kill mice and rats for a long time, it's been on the market for many years. However, where I use it, it can only be accessed by rats and mice and never is there a chance that other, non target species get near it.
I think the neighbor just needs to put that poisen in a place where only the intended targets can get to it. . .
Good luck,