The problem is not so much factual/nonfactual content as the opinion and contextualisation, as well as the choice of stories. You can generally tell the stuff that's at least trying to be an objective report because it's syndicated AP/newswire content and is substantially identical across the different news sites.

But there's no real boundary between that and the opinion.

e.g. opinion: http://insider.foxnews.com/2017/09/26/tucker-carlson-battles...

news: http://www.foxnews.com/world/2017/09/27/mortar-rounds-land-a...

(both items selected from the Fox front page above the fold at time of writing)

The simple act of deciding what is and is not "newsworthy" is not objective and cannot be made objective. So truly objective news is impossible.