I could see the news working heavily into the game if they ran with that idea. Like, you see a story about a drug bust taking place, then if you go to where the bust happened you can find a closet or a crate with guns and money inside that you couldn't have accessed if you hadn't seen the story.
Or, you could see a story covering the fallout of a mission you just completed and based on what you find out, certain aspects of the next mission will be different than if you had just gone straight into the next mission. Like, if you killed someone in the last mission whose son you were supposed to kill as part of the next mission, the news will say something about the son going to the funeral, and you'll have to complete it without killing him, then there will be a different mission later where you kill him. Or you could skip both missions and just kill him at the funeral, which would give you the opportunity to kill certain people you were going to go have to go after in the future.
Maybe that's too complex for them to do, but it would be a really creative approach to the game and there would be incentive to watch the TV.