It's a management failure. The employees are not going to magically get excited and proactive about PR just because some out-of-touch Internet marketing celeb thinks they should. It's management's job to make sure people are trained properly in how to handle these situations, and also, more importantly, to provide the clear vision and incentive that makes people care. Finally, if employees are hurting the image of the company, it's management's job to fire them.

If a random employee starts taking up issues caused by other people in the company, and there is no culture of communication or escalation procedure then one likely outcome is that they are going to waste their time and not get their job done. That doesn't mean an employee shouldn't be proactive or whatever, but just that in a large organization the solution can not come from the bottom up.