A better way...
Even the stories from major networks that wouldn't fall under the hoax or satire category can be untruthful or misleading (See MSNBC, aka: More Silly Non-sense By Communists). A better option would be to do the opposite, encourage fake stories. The more hoaxes people are reading and then finding out they were indeed fakes will train them to be skeptical about what they are reading on the internet and hopefully prompt them to seek out the actual truth.
This change may lead people to "let down their guard", if you will, because in the back of their mind they have the idea that facebook isn't posting fake stories anymore.