The ringlet type Barred Rock, which we also own, is the great example of what a Barred Rock should be, according to the standard. This is the aspiration or the goal of Rock breeding. What passes for a Barred Rock in most cases is a bird that is so far from true type that it would be disqualified if judged. In most cases, it isn't even within a country mile of the standard.
The reality is that just because a bird is 40% Barred Rock, just enough to sort of, kind of, look Rockish, (to coin a word) doesn't make them a true Barred Rock. Most BR shown here on the forums (what you called "a typical Barred Rock") is merely a partial Barred Rock. But, this could be said of most of the birds shown and said to be this or that breed.
Are they chickens? Of course. Maybe even great and wonderful egg laying chickens, but hardly an honest representation of the breed, just kinda, sorta a poser of the breed. Doesn't make them useless as utility birds, meat or egg sources. It takes awhile, sometimes, to wrap one's mind around what a "Breed" is. A breed is a chicken that mankind developed. They were often blends of different foundational birds, worked on by many people faithfully for many years, and when 100 of such birds could be successfully shown to the poultry world and bred true, an application was made to the American Poultry Association. An artistic impressional drawing was made of the ideal bird and a standard was written, specifying, with great detail, the physical features of the bird. Then, and only then is it declared an accepted breed.
The standard for the Barred Rock calls for such barring as you see in those famous drawings. In a perfect world, all Barred Rocks would be as crisp. That's why it is called the Standard of Perfection.
