I guess what wasn’t clear was whether the back yard was fully enclosed or not. If it wasn’t, she did what I consider reasonable, leave the dog on a long enough tether to be able to move around, but not get off the back yard. One should be able to be safe in one’s own backyard, whether you are a person or a dog.
But the sheriff still had no business in the back yard, he just left his card at the front door, he could have done that to begin with, instead of going to the back yard, where the dog was. Also, since the dog was tied up, he could see how far the dog can go and as long as he stayed out of that range, he was in no danger from the dog. So there is no justification for what he did.
But it’s not good. Neither for the dog NOR possibly innocent bystanders.
I have a long story relating to dogs left outside completely unsupervised, albeit “restrained”. I gave the owner an earload of how those dogs were not only a threat to us but how he was basically abusing them at the same time.
Then we'll just have to disagree about what is reasonable. If there's nobody home, I don't consider that reasonable. Both as a military police officer, and as a volunteer at an animal shelter, I've seen too many dogs tied up and left in a yard who either wrap the tether around a tree or get it tangled on something and can't get to their water on a hot day, kick their waterbowl over and spend the day without, hang themselves over a low fence, get mauled by a stray dog or pack thereof, get abused by passers by (with or without badges), or eventually contract heartworms from being a veritable cafeteria for mosquitoes. etc.
If you have to leave your dog tied up outside while you go to work all day, you either don't have enough respect for the animal, have too big a dog for your residence, or haven't invested the time and discipline in training the animal that a responsible pet owner should. A fenced outdoor run with shelter and water is entirely different, ut tying or chaining them to a tree, a post, an anchor, etc. and leaving for the day is simply irresponsible.