By stopping participating in discussions about facts vs "facts". The above publications don't have a particularly stellar record of clearly differentiating between the two in a way that those who lack excellent critical reading skills are able to leave with an accurate perception of what is proven vs alleged. But this is a matter of opinion of course, the level of criticality one applies when reading the news typically varies according to the political topic.
How do you check out? By going to a reputable news source, like NYT, WaPo or The Guardian?