The legend of the Dorian Invasion would be a good example of this. The Ancient Greek literary tradition held that Spartan rule over the region of Lakedaimon was established during this Invasion (also called the Return of the Herakleidai), in which the Dorians (to whom the Spartans belonged) descended into the Peloponnese and drove out the local ruling classes. This was supposed to have happened at some point in the distant past, possibly in the 10th century BC. It gave the various Dorian peoples of the Peloponnese an epic origin story, and explained why local dialects had disappeared in favour of Dorian Greek by the end of the Greek Dark Age.

In theory, it seems plausible enough that this legend would go back to an actual historical event. Mass migrations frequently lead to the replacement of one ruling elite with another, and incursions from the Balkans into mainland Greece were certainly not uncommon in later times.

The only problem is that there is not a shred of archaeological evidence to back it up. There is no sign of violent conflict, no evidence that the material or civic culture of Lakedaimon changed dramatically during this period, and nothing to suggest that its culture became different from that of other Greek areas.

For this reason, scholars now assume that the idea of a Dorian Invasion was an explanation invented by the Greeks in hindsight, rather than a surviving tradition about a real historical event.