Why these stories (and the pebble technique from the article) work is that they enable kids to predict what the consequences of their actions will be. They can't do that without at least being told what they would be, and when they're violent, angry and panicking (ie. during violence) is not the best time to learn.
Violence is mostly the result of losing control. And most parenting strategies boil down to immediately using more and stronger violence to stop whatever behavior parents don't like. This, of course, prevents the kid from exploring that behavior, and of course teaches that an immediate escalation of the violence is the way to go (which is how you very often see kids behave to eachother). You should always let kids fight until one actually gets some small amount of actual physical damage (enough to, say, make them scream, at least), before interfering. If you have to interfere before this point (e.g. involving the eyes), you have to tell them not just not to do it, but what would have happened, and then answer their questions on it. These questions will be very cold and direct ("Why can't I poke out her eyes ? She stole my doll !") and that does NOT mean your kid is evil.
You might say "parents don't use violence". No ? Dragging kids physically away from whatever they're doing. Limiting them to their room. Going to bed without dinner. I'm not saying these are always bad things to do, far from it. In fact after doing what I suggest you do, I think dragging kids away is not necessary, but some measure of punishment should probably still be demanded, AFTER explaining the situation AND answering questions about it.
The problem with the western way of protecting kids before they get into trouble is that this escalation by parental violence (physically preventing the child from doing anything wrong and/or "evil") is that it doesn't work. Sometimes YOU are wrong. Believe it or not, it happens. Sometimes the teacher IS WRONG. Sometimes the police is outright evil (or at least morally questionable). Sometimes multiple parties may be wrong at which point "who's at fault" is probably a stupid question.
(e.g. kid lends toy to kid2, kid2 insults kid, kid demands toy back, a fight ensues, parent intervenes, kid still fights to get toy back, parent's hand hits the table, plates break and chair falls on kid2. Who's at fault ? Technically the insult, then not giving lended toy back, then trying to physically get the toy back and presumably the parent could have been more careful too. All participants are "at fault", BUT I guarantee you not all will be punished)
What you have taught the child is, in that case, to immediately escalate the violence. Guess what ? You're not going to like the result. And of course, this cannot be understood, and what do we do ? Escalate AGAIN.
If your kids fights you, fight back (MEASURED of course, I'm not saying knock them out). If you do this when they're 5 you can keep the fight perfectly under control and they will get the point: they shouldn't fight their parents because it's not an effective strategy to get what they want. Again, questions will probably follow, and they'll really learn something.
A kid should NEVER be taught to react violently to enforce some standard of "justice", but that's exactly what we do. And now you might argue, but justice exists, doesn't it ? One, there's the philosophical point that no, it doesn't. Two, you don't have the information to make correct judgements about what is just or not. And three, just or not, it is more important that the situation remains livable for everyone.