I can tell you that at least some dog urine will kill flowers or cause brown spots on grass and shrubs. I don't know if it is just some dogs because of what they eat or if it is all but the urine does kill things. I don't get why if you are walking your dog on a leash that you can't pull it away from other people's property if it starts to go. I also don't think dog owners stop to think or they don't care that once their dog pees every other dog will want to pee there. That concentrated urine in a spot in your neighbors yard is probably a lot more than in the dog owners yard so maybe the dog owner doesn't understand the damage. I still think it is beyond rude for an owner to walk your dog away from your yard to let it damage someone else's yard.I'm not a dog owner. I'm sure letting a dog pee or poop on your grass might cause some discoloration, but I really don't see why it is such a big deal if the owner cleans it up. Maybe people are just good about it in our neighborhood, but I rarely see poop when we go on walks. I've never met a dog that liked going on cement and there are no public gassy places. Where are they going to go? You're going to ask Fido to politely hold it until you get home?
I completely understand being annoyed if the evidence is not picked up.