In Homer, mythos means speech, word, the thing said, with no falsehood attached. Herodotus treats mythoi and logoi as interchangeable terms for accounts he reports. Through the classical period, logos, the reasoned, checkable account, was raised as the standard of truth, and mythos sank to mean the unverifiable, then the fictional. By the time the word reached English, the execution was complete.
The philosopher who policed poetry out of his republic also invented the Myth of Er, the cave, Atlantis: stories he flagged as stories, told because, as he wrote, some truths only fit in them. His readers have argued for two millennia about which parts he believed.
The theoretical reading: mythos did not lose a fair fight. Philosophy, and later institutions built on it, redefined truth as whatever logos could certify, and everything older, oral, sacred, communal, was reclassified as fiction. The modern fact-check, on this view, is the same move: not wrong about the facts, but blind to what the story was carrying.
Plato invented myths on purpose and said so, because some truths, he wrote, only fit in stories. If the philosopher who demoted myth still needed it, what exactly was demoted?