Though I've read it twice to understand perfectly what you're saying but I think over hyping makes more sense than de sensitising, and you have said it all too.

To quote you "over hyping things could be far more dangerous. People who are de-sensitized to risks are more prone to dismiss potential danger**".

It's better safe than sorry for them too, what if it wasn't hyped and many took it for granted, only to later sue the media for negligence of information. How do you see to that.