Fact checking isn't subjective, though. You either do fact-checking or you don't. If you do fact-checking, you're either checking if the statement is factually correct or not. There is no real in-between and no real "this is true because I think it is."

At least from a human perspective. You're right in raising the concern that from a machine perspective this is hard to achieve, but again that's a red herring to the OP.