There's no garauntees in anything. One can only try to properly prepare in order to try and tilt the scales in their favor.
I'm not saying it would "prevent" any occurance, but if the parent had run a background check it is possible they would see something that made them uncomfortable and therefore would not enroll their child and put them in a dangerous environmnet.
That sounds very unusual. Do parents and consumers run background checks on professionals in your state? I don't know any state in the country that supports that level of intrusion, but I've been wrong before.
Here in positions that require background screening, it is done at the time of hire and tthe only people with the information is the individual's HR department (or hiring manager if there is no HR). FACTA laws apply if HR garnered the information from a reporting agency. Background checks are rarely done after the point of hire so someone hired in 1995 that was busted doing something illegal 2 years ago on vacation in Vegas may not get caught unless they change jobs.