The short answer is, we don’t, since by their nature there’s no way to check them out. There is, of course, a longer answer — which is why this question gets its own page.
When authors submit their stories, they warrant (that is, promise or swear) that the stories are true, and that they know the facts first-hand. So, first of all, we’re relying on the authors telling the truth when they give us their word. Since part of the premise of HeroicStories is that, in general, people are good (the public sometimes thinks that people in general are bad because we usually only hear about the “bad” ones in the newspaper or on television), we consciously choose to give the authors the benefit of the doubt.
But there are always people who will try to “test” the system to see if they can pass off fiction as a true story. And you know what? That’s fine — if they really want to present themselves to the world as liars, that has to be up to them. If we see obviously fake stories, we’ll reject them. But when we see stories we like, with a point, that might inspire others to Do Good, we’ll happily take the risk that the story may be embellished, in whole or part. We can live with that.