I don't think I'm going to watch the video after seeing the responses here; I can't really stomach images like that. I will say I agree with the sentiment there are plenty of alternative options that should seem fairly obvious to professionals (e.g. cops) who may encounter such situations.

I got a call last fall from Aurora PD that my neighbors reported seeing two people leaving my house carrying bags. The thieves opened the gate, waited for my dogs to run out into the yard, and then went into the house to rob me, closing the gate behind them. They were long gone when the cop showed up, but my dog (a breed famous for being violent and aggressive) was standing on the porch growling and snarling at the cop. The cop sat in his car and contacted animal control and later told me he wasn't going to try to go in the house to see if anyone was still in there. When animal control showed up, they and the cop chased my dog back in the house... no shots fired, no harm done. Despite how often we hear these stories, I'm glad there are still LEO out there with a good head on their shoulders.

Dogs protecting their property are doing their job; it's one of the primary reasons I have dogs to begin with. It's just a disconnect in logic to intrude on the dog's territory and then shoot him for challenging you.