Because Stone would milk the political angle the story provides for all its worth...plus he's great with emotional scenes ("Born on the Fourth of July" springing directly to my mind.), he's not squeemish if the story asks for some stronger imagery, I think he'd have the right visual sensibilty for the material and to top it all, he's great at getting good performances out of actors you'd not imagined coming from the likes of Tom Cruise or Woody Harrelson.
That's just my take, of course....