On a more serious note, I can see validity to both sides of this debate.
In just about any unintentional discharge situation (with the possible exception of a mechanical failure that could not be foreseen), there is an element of negligence. We seldom have any trouble finding at least one of the 4 rules broken, and usually these events involve the violation of 2 or more of the simple standards of conduct that have been established to prevent these incidents. These lapses in the basic, responsible behavior that anyone who owns or uses firearms owes to the rest of the community are, in my opinion, clearly negligent conduct.
The argument for calling them accidental has to do with the lack of intent on the part of the shooter. This element is not always clear. When someone kills his girlfriend by pointing an "empty" gun at his girlfriend and pulling the trigger. He then tells the investigators he was cleaning the gun, didn't know it was loaded, and it was an accident. Negligence in this case is clear but lack of intent is not, and I lean toward treating such cases as homicides until proven otherwise.
I would apply the term "accident" to an intentional discharge where the shooter reasonably believed he was complying with all 4 rules, and an unforeseen circumstance caused an unintended result. Example: The shooter fires at an identified target in front of a large earth berm he has used as a backstop on many occasions. This time, the round hits a small rock concealed just below the surface of the dirt, ricochets, and strikes his shooting companion.
In the recent post where a teenager pointed his .380 at his thigh and severed his femoral artery when the gun fired, it appears he did not intend to shoot himself. I think we can legitimately say that the end result was accidental, but the behavior that led to that result was negligent. The trigger did not pull itself, and the potential for injury when one points a loaded gun at a body part and pulls the trigger is a hazard any reasonable and responsible person would foresee. Not checking the gun to see if it is loaded doesn't reduce the negligence factor.
I could accept classifying an incident like this as an "unintentional discharge due to negligent action with accidental results" if you want to put a really fine point on it, but IMHO, negligent action is clearly the cause and we shouldn't sugar coat that with terminology that lifts the burden of responsibility from the actor and allows folks to place the blame somewhere else, like on the hardware, the manufacturer, the seller, or the ammo maker.