Maybe it's so obvious you can't see the forest for the trees.
Media generates interest. Big-time sports is an entertainment industry; as such, they are competing with the many, many other forms of entertainment out there for you attention and dollars. So your company - in this case the NFL - needs publicity. And they get it - for free - from the media.
If you're going to make the argument that the NFL is "too big to fail," then you've got to account for the fact that once-holy forms of entertainment - say, the movie industry - are shrinking. Baseball is concerned about being left behind, too.
So yes, the NFL needs the media - and the media needs the NFL.