It can hurt. And it can put you out of business. Businesses are measured not by what actually happens during a time of crisis, but by public and other perceptions of what happened. Most everyone who is important to your company will learn about your crisis first through the news media. The first information you get about your company's crisis is almost always wrong, so double-check everything .
People are people.
They get excited, and report what they think they heard. They shamelessly and quickly spread inaccurate information. But if the company's procedures are weak, and it leads to people getting hurt, sick or killed, it's a different matter. The public can't forgive you until you say you're sorry. Prepare some sample media statements for those scenarios, too.