As an alternative, since you brought up primary sources, you could always show a case where one of the news outlets I mentioned took a story from somewhere else

As an alternative, since you brought up primary sources, you could always show a case where one of the news outlets I mentioned took a story from somewhere else, who took it from somewhere else, who either made it up or turned the chain of citations into a self-referencing circle. That would be a perfectly acceptable demonstration of "fake news" that would draw me in to listen to your side of things. All it takes is a little evidence.