And right there is where the problem is. No matter how differently they report things on News Night, the differences can't have consequences, because they can't change how things actually played out in the real world. They will end up demonstrating the opposite of your thesis -- no matter what they do, nothing will change, because nothing did change.
Using stand-ins for real news stories the way they did on The West Wing allows consequences to be explored. The United States involves itself in negotiations between Palestinians and Israelis, and ends up sending a peacekeeping force of 20,000 into the Gaza Strip. The consequences of this fictional involvement affect the show's characters and their decisions. It didn't happen in the real world, but in the context of the fictional show it's more "real" than the Giffords story on The Newsroom was, because no matter what Will reports about Giffords, nothing can possible change. They choose not to report her dead, and... what? They feel vindicated. And that's "reporting the news [having] consequences?"