Michael Pearl tells one mother on his website, "I could break his anger in two days. He would be too scared to get angry. On the third day he would draw into a quiet shell and obey."
This is the first I've ever heard of the Pearl's.
I've never read their book, never been to their website before today, I don't follow their teachings, I'm not a fundamentalist Christian, heck, I'm not even a Christian.
But like most things taken out of context the quote above, and the rest of the discipline techniques cited in your list, as cited in your list, are misleading.
Here's a full quote from the website beginning with the comment I've cited and continuing on:
I could break his anger in two days. He would be too scared to get angry. On the third day he would draw into a quiet shell and obey. On the fourth day I would treat him with respect and he would respond in kind. On the fifth day the fear would go away and he would relax because he would have judged that as long as he responds correctly there is nothing to fear. On the sixth day he would like himself better and enjoy his new relationship to authority. On the seventh day I would fellowship with him in some activity that he enjoyed. On the eight day he would love me and would make a commitment to always please me because he valued my approval and fellowship. On the ninth day someone would comment that I had the most cheerful and obedient boy that they had ever seen. On the tenth day we would be the best of buddies.
I can't necessarily say that I completely disagree with what I'm reading here.
I would argue that while my parenting techniques are somewhat different than Mr. Pearl's they also include pain and punishment, have invoked a healthy sense of fear, and are very, very rarely even necessary any longer.
When my kid acts up I count to three.
One...
Two...
I can't remember the last time I've actually gotten to three. It's been a good two years, maybe longer.
My boy, six-years-old, knows when I mean business and he knows not to try me.
He rebels at times, and I think it's only natural that he does, and I tolerate it within reason because I think pushing the bounds of authority and asserting one's self are healthy and help a child grow into a self confident adult.
But it's no secret that kids also need boundaries and structure to grow into secure, self confident adults and you don't get secure kids by providing wishy-washy boundaries and guidance.
I get to see plenty of push-over parents and their children through my boy's school and sports teams.
I have to say that I'm thoroughly unimpressed by most of their behavior.
I don't think it's a coincidence that I'm stricter, firmer, and perhaps more "hands on" (so to speak) than almost all of the kids my son associates with, and the fact that parent-teacher conferences go something like, "What can I say? He's a bright boy. He's obedient, helpful, gets along with the other kids very well, listens when he's told to do something, and is reading at a first-grade level" or "He's the most athletic kindergartener in the school, and one of the most athletic kids in the school. I have to pair him with the first grade boys because he runs circles around his classmates. He knows the rules, asks for clarification when he doesn't understand them, and makes sure to enforce the rules when he sees them being broken".
That's not to brag, because it's not bragging when it's true.
That is to say that when you spare the rod you do spoil the child.
That's as true today as it was 200 years ago.
I really think that must be the message of the Pearl's book, from those quotes from the book (full quotes, in context) that I've been able to find and read online.
I think the parents in the OP article took some very good advice and went so far overboard with it that it resulted in abuse and murder.
I suspect, though I have no way of knowing, that those parents are probably not a great deal different than the hundreds of thousands of parents in America every day who are physically abusive, and whose abuse sometimes ends in murder, but who have never read this or any other book which treats on strict parenting which advocates for some degree of corporal punishment.