The purpose of tapping during training is to say "I've reached the physical limit, any more and you will injure me." causing pain in the dojo is fine and expected but injuries need to be avoided. Injuring someone to " toughen them up" is idiocy as all injuring some one does is make them weaker. It is unacceptable for a person to ignore someones tap out. That's negligence and could open up the whole school for lawsuits. Some idiot hyperextended my teachers elbow and it never healed properly. Don't let that happen to you.
There's a lot of truth here -- but sometimes, an instructor does know that the student is tapping too quickly, and may hold it slightly longer or go a little further to show them. That said -- the action should be paired with an explanation, especially if it's a case of a student tapping WAY early (I've had students tap almost before they were even touched...). It shouldn't be a routine case of "I tap, teacher puts me in extra pain."