"Whoever spares the rod hates their children, but the one who loves their children is careful to discipline them." says Proverbs 13:24 and if the kid is severely injured or dies in the process, well that's ok because it's the Bible telling parents to do so.
First of all it's certainly frightening that a book like To Train Up a Child could be popular around the world. Responsible parents don't train a child, they educate a child, but apparently Christian parents tend to leave it up to God to educate them and I don't see that as being very responsible.
The "observing Christians" (which is just another way to say "religious freaks")who authored the book hold the typical arrogance of the preachers who actually believe their actions are manifestations of God's will, that Gods acts through them, and that whatever they do or say has a part in God's plan. Therefore, they won't see anything wrong in their message or the consequences such a violent and abusive message has. I bet it took the reporter a lot of self-restrain not to punch both of them in the face when one of them started hitting him lightly with his hand.
According to the authorities, the girl was beaten for seven hours with short breaks for prayer. I wonder what kind of person could pray, and what those prayers would be, before and after beating a child. My guess is that those parents also thought they were doing the correct thing because if God says so, well, how could it be wrong?
To regard the Bible as the word of God is to be nothing else but a card-carrying idiot. Sure, it could contain some interesting and useful content, but to obey it word by word because of its supposedly divinity is plain stupid. These kind of cases remind us that the idea of a God talking to people is a really bad idea and should be fought against if what we seek is a more rational an peaceful world.
Finally, if really God meant what that couple did and didn't lift a finger to stop them, He/She is huge dick. Or he just doesn't exist, which is the most probable.