I hope you are fortunate enough that you don't have children who have any behavioral issues. Not all kids are the same, and not all techniques work. I have seen two in my immediate family that were exceptional cases. One eventually overcame it. All of the "normal" options did not work. My sis and her husband had raised two others with ease and great parenting skills. The third one would have none of it and was violent and non-responsive to all of the traditional methods. Once they faced down their personal distaste of physical punishment and starting using corporal pusnishment and other more physical options, he got the message. He's now a fantastic teenager. He wasn't abused.
My other nephew wasn't so lucky. He is bi-polar and ran the gamut of regular parenting, tough-love physical punishment, drugs and therapy, even military school and boot camp. No matter how hard his parents tried, nothing worked. He became a violent young adult and will be in prison for a while. I think he's doing 15 years or something for beating a friend nearly to death.
So the point is, every situation is different. I can't say that because your kids respond to one type of parenting, that it's the only way to parent. I also don't know the history of this woman and this kid, so I can't say what the "context" is. But I don't believe she has done any physical harm to her child that warrants police involvement.
I can say, though, that I believe teaching discipline with physical ramifications is a far better option, in my opinion, than say... loading kids up with fucking drugs to "level them out" which is what seems to be the first parental option of choice in way too many cases. Drugging children is much more "abusive" to me.