Oh, bull crap. By this argument, literally no protection or liberty that allows even one child to be harmed could ever be tolerated. Why stop at vetting baby-sitters or teachers? We ought to require mandatory background checks for every person who ever visits a family or goes into a public space that might contain children. Law enforcement also ought to be able to track every underage child at all times, via mandatory GPS collars.
At the risk of sounding callous, there are occasionally some situations where you really do need to shut up and multiply.