@Dave Bell
You forget that the citizens are now sow cowed that they will all line up in an orderly fashion and each take one, and only one, carefully measured dose.
Just remember that these people are selling fear, not information. The bigger the numbers. the more the fear. Saying "might kill a few and make a few more sick" will hardly win them airtime or a position at the big table of power.
Also, these people have no real reason to fix the problem. If the problem goes away then their power goes away. All up, it means they have a vested interest in making the problem seem bigger than it is.