It is fundamentally bad writing to have a character display knowledge that it is impossible for the character to have -- and in this case it's particularly egregious because it's so completely opposite to how a character in her situation would be more likely to react (e.g. "Oh, you save the hot reporter, but where the hell were you ten minutes ago when hundreds of thousands of people were dying all around me?")
Well actually a more plausible reaction to Superman in the aftermath of that would be "Ahhh! It's one of them!" Run!"
One of my personal disappointments with Man of Steel is contrary to the filmmakers central thesis with the film: "How would people react to a levitating super-human who could shoot layers out of his eyes?" We never had a reaction from normal, everyday people to Superman's first appearance. I hate the idea of having Superman first don to suit to fight an alien invasion as opposed to the traditional idea of him first doing it to stop an accident from happening. If Superman existed in the real world and started flying or whatever I would expect people would be somewhat dubious, scared or just confused. How wonderful would it have been for the film to actually follow through on what was set up earlier in the film with Jonathan Kent exclaiming "People are afraid of what they don't understand." Why couldn't the film showcase the conflicting or mixed reactions of the people towards an alien being? The only reaction we get towards Superman from the people is Jenny(who's an awful character, where's Jimmy Olsen?) This would add to the introspective crisis Clark faced and further raise the deep, internal question: Can he ever be accepted? I think it's the film's biggest failure from a story standpoint IMHO.