It is not uncommon for people who are sexually attracted to children to take up professions where they have access to children. The screening in response to this is not so much “hysteria” as it is reacting to a real problem.

Note that “only present for one day” overlooks the practice of grooming. Nobody is suggesting that putative-molestor is going to molest the child at the school during the reading. They are suggesting that when an adult is formally introduced to a child under the auspices of the school, thus giving the relationship official sanction, it is good to be reasonably sure that the adult doesn’t have an ulterior motive.