^^There is a certain amount of truth to this statement.^^
I don't even begin to know what to tell you. Where I live, I think I'd have a chat with the Twp Trustee's and let him know my concerns. Maybe they can at least advise you on the laws.
I have a German Shepard that I let run in my yard. But he knows to stay in the yard and I broke down and bought a GPS collar. So if he does leaves the yard, I know it right away. My neighbors are all okay, and I'd like to keep it that way, that's why I bought the collar.
I agree with your concern about the dog. I was a mail carrier, can't tell you the number of times people told me their dog was was "okay", only to have it go ape when they weren't around.
I hope it works out for you, good luck!