Peter Sandman says it is officials, not citizens, who needlessly panic:
If you ask yourself which was a bigger problem in New Orleans, people so frightened they couldn't think straight, or people insufficiently frightened who didn't get out of town, I think you can make a very strong argument that the latter was a bigger problem than the former. … In the stairwells of the World Trade Center, people were more courteous than New Yorkers usually are, and more organized than New Yorkers usually are, and there were very few signs of panic among those who evacuated the Twin Towers. . . . When you interview the survivors, the vast majority tell you they panicked, but they didn't. They're wrong. They felt like panicking, and they did just fine.
Panic is quite rare. What's quite common is denial; denial is why panic is rare. … If people are insufficiently afraid, they don't take precautions. If people are excessively afraid, they don't take precautions. They don't panic either. They go into denial and sit around saying, "It'll happen to somebody else."
So why do officials needlessly fear public panic? I suspect what officials really fear is that citizens will blame them for whatever bad thing is happening; the panic thing is just an excuse to avoid looking bad. Hat tip to Tyler and Toby Ord.