Letting the deputy do it even after the deputy stated he didn’t need any proof shows that the owners didn’t know about their rights under the law. Something like not presenting the dog to the deputy probably never occurred to them.
This sounds like a rural area where the guy with the gun and badge is the law, and few people understand the sort of law that the rest of us take for granted.
This particular guy with a gun and badge is in deep legal trouble, because with wide publicity, the incident has certainly come to attention of those segments of Idaho society where more advanced concepts of law prevail. He is also amazingly incompetent with a gun. Three rifle shots to a tied-up dog, with intent to kill, and the dog lives to tell the tale ??? If the guy has a family, I sure hope they don’t expect HIM to protect them from home invaders!