Your perception of the studies are all wrong. Most places allow corporal punishment. CT does. The studies simply say it is less effective. But physical discipline is provided like you did it. A parent, in control of their emotions, doing enough to send a message. Welts and bleeding are not discipline.
I was hit as a kid and I don't feel I was abused. But I've raised 4 respectful kids without a hitting and 3 of them were very damaged foster kids who had serious behavioral/emotional problems.
Not to you but to warrior & CT. Child abuse is against the law and by definition, not a personal matter. Kids die and are scarred all the time. Just like you can't beat your wife, no matter how much "discipline" she needs, you can't beat your kid. But these cases are not usually dealt with in court. Parents are provided services to improve. Only in pretty extreme cases (not AP) do these go to court, and then it is to terminate parental rights.
Working with kids my whole life, it always amazes me. If AP had done this to a dog, people would totally freak out and demonstrations and petitions would be everywhere. But kids, they are just property. We should all mind our business.
Crazy!