That's the thing. Even if the mother gave permission, corporal punishment is not legal in this particular county so why would the principal choose to paddle the child? Presumably the principal is aware that this is not permitted, yet she has a paddle in her office ready for use.
I think that's why this is such a hot discussion. Yes, this was not allowed at this particular school so the principal was in the wrong, but corporal punishment is permitted in 19 states. That means that a good percentage of the country do not believe that it's a parent's duty to protect their children from this type of thing, but instead believe that this is a proper form of discipline that is acceptable to use in a school environment.