The fact that people are upset by it could be reason to hide it away, though, to protect the sensitive.

I don't think hiding it will prevent people getting upset. In fact, hiding it may make people more likely to believe it, and thus get scared. If someone respects EY and EY says "this thing you've seen is a basilisk" then they're more likely to be scared than if EY says "this thing you've seen is nonsense"