The alternative explanation is that God created stars. And that He did it such that they seem to create heavier elements through fusion. But that's just an illusion. Because, you know, the Universe is only 5000 years old.
And that alternative will pass fact checking, unless they exclude literal readings of the Bible.
But as others have pointed out, choosing accepted fact checkers is subjective and contentious. Do we then need fact checkers about fact checkers?
Many claims have moved from conspiracy theory to fact in recent decades. Now there's a class-action case about CIA experiments with LSD, and the principal investigator will testify. Before Snowden's leaks, how many people thought that the NSA was intercepting so much stuff? Consider allegations about using poor people to study effects of terminal syphilis, measure Pu excretion rates for body-burden calculations, or look at symptoms of lethal full-body irradiation. Which of those (if any) are unconfirmed conspiracy theories?
Because some people believe them to be the ground truth? Any "fact" that contradicts their understanding of their favourite religious passage is obviously fake news. Dinosaurs? Fake. Evolution? Blasphemy. Round Earth? Idiocy...