In the example above, the speaker said:

the real problem is the way that the media has handled this

Of course, you could also say:

the way that the media has handled this is the real problem

So why does the speaker use the first version? It's because, in English, the information that comes at the end of the sentence is usually the most emphasized. We usually start a sentence with a subject that the listener or reader already knows about, and end with the subject that's new or needs to be emphasized.

In the example above, "the problem" is something that everyone is already talking about, while "the way that the media has handled this" is the speaker's new opinion.