I guess I'm a "meanie" because I do not like for my neighbors to allow their dog to potty and/or poo in my yard....which they used to let her do both in our yard and then take her back home.
It does burn the grass and causes brown spots. Even if it's the part of the yard that the city owns (between the sidewalk and street), I still think that is rude because it is part of the look of the rest of your lawn. My city doesn't take care of this part of the grass, even though it technically belongs to them.....my husband completely takes care of it, just like the rest of our yard. I just, personally, would not allow my dog to potty anywhere even close to someone's yard.