Fact checking is simply applying some standards to information. People do this in their own minds every day. Outsourcing it to others can be dangerous, but it's not inherently so. If you choose to believe something you read, you're placing your trust in someone else - a news organization, government, friends, family, whoever. If an organization set up for fact checking has published standards and list the violations of those standards when they deem something to be false or misleading, then why shouldn't you trust them? To be clear, I'm not suggesting Facebook fits the bill here - you attacked the very idea of fact checking, which, when done right, is a valuable thing to have in society, unless you just literally trust no third parties that present information to you.
