This is related to the Streisand effect. In this case, they aren't trying to hide/censor anything; they are trying to re-assure people. But saying "things are okay" causes people to start wondering what would be "not okay" -- and it turns out that the current situation is more "not okay" than "okay".

To make matters worse, very few people have any understanding of what banks do. Most people think it's just a place to store money, which is like saying that a car's fuel tank is only used to store fuel. Bank runs are the result of people assuming that savings and checking accounts are risk-free -- and the bank-runs begin when people realize that those accounts are far from risk-free.