Here it's "any dog" as well.  
My neighbor's 2 labs came over one day, nothing menacing they didn't even notice the bunnies, they were too excited getting petted to care (my kids have met the dogs before).  Walked them nextdoor, and owner apologized, and fixed the fence the next day.  He's a rational man, we get along good.
Neighbor across from me has 7 purse dogs, a hole in her fence that they get out of and ignores it when someone says "your dogs got out", it's a daily thing.  She seems to think because they're small that they get to run in a pack and poo on everyone's lawns.  If I found one of her dogs trying to get in my pen, I would not be so gracious.  Now I may take the dogs to a shelter as a dog that roams the neighborhood (none are tagged or collared), but I'm not inclinded to hand her the dog back either (last guy that brought home an escaped pooch got screamed at for "touching my dogs").