I love the natural instinct to protect family that GSD's and similar breeds have. Our dogs have never hurt anyone or anything and when we take them to the dog park they run and play with all the other dogs regardless of their size or if the playing gets rough. On the other hand they can sense when something isn't right and react accordingly.Not gonna watch the entire video because I think the basics were covered in the first few minutes. I don't think that GSD is feeling remorse at all. I think she's picking up her owner's vibe through his tone of voice and other body language that says he's disappointed with her. I agree with @Gadsden this is a person problem more than a GSD problem.
In my opinion, it's common sense that large dogs that are generally bred for protection have the ability to kill/maim other animals or even people. I've had several JRTs and, pound for pound, they're one of the most efficient killers of small furry creatures on the planet.
I've never had a dog that was aggressive towards people. But almost every JRT I've owned has had a natural tendency to hunt and kill. You can train away certain behaviors but not completely. Large dogs are still very capable of being aggressive, sometimes for reasons only the dog knows.
My son in AK has a heeler that's very aggressive with strangers. I spent a week there in June and the dog wound up biting me on the foot. Not really a serious bite but it wasn't pleasant, either. It could be a real problem when that dog bites the wrong person. I really worry about what that dog is capable of.
A few years ago my wife had taken one our male GSD's out to the park when a man started approaching her from the other direction. Kona sensed something and moved from his heal position to in front of my wife and immediately sat down and stared at the guy as if to say, c'mon, I dare you. She said the guy took one look and went off in another direction. Kona had never done anything like that before and he had gone on lots of walks were it was just the two of them.
But truth be told there are some dogs who, for some reason, have a natural tendency to bite and for whatever reason that urge can't be broken, but I think those are isolated cases and the majority of problems stem from the owners. Heck, truth be told the 'meanest' dogs I have come across are the ankle biters. Granted they don't do much damage, but I couldn't tell you how many times I've been bitten by some chihuahua or some other little runt on four legs when responding to someone's home.