Not sure it's really a matter of trust. People just like juicy, sensational stories, and stories that cater to their weaknesses. National Enquirer has been in business since long before Facebook.
How long do you want to spend on a site debunking stuff? That would not be much fun. Moreover, what would be the effect? Ideally, people would adjust their news filters and start to critical think for themselves. I don't think I've the right educational credentials for that. :-)