The hardest part of this would not be restricting 'Factual' news to sites that label themselves News, it would be determining who decides what is actual truth. It would seem simple to just get the actual story and present that, but any story with two people involved has 3 different stories.
Story from person A
Story from person B
and the truth
Even when news agencies try to provide both sides of a political story, it is obvious that the writer leans towards one truth of the story, either by limiting the other side or even getting quotes that don't reflect the other side of the story. So, it would take several back and forth questioning to get all sides of the stories in order to put it down in a manner that was as close to the True Story that happened.
The biggest hurdle to acceptance of this new way of getting news, will be that people will know that the News site is the story and is factual, but they would rather get it from the other place, because it will have information faster and more in-line with what they think the story is.