As some one who works in a daycare I have seen kids get hurt doing the same thing and some kids barely have a scratch and some have bruises or cuts. Also want to point out since schools are not paddling bare bottoms (would be super wrong) so the school employes would have no clue if s/he is doing it to hard.
Some medical conditions and medication can make the paddling more severe and easy to nasty bruises welts or make the child bleed.