Plutarch (the source of the quote) was born around 50 A.D.

The Battle of Thermopylae happened in 480 B.C.E.

That's more than 500 years of oral retelling and (possible) embellishment, as told almost exclusively by the victors.

Historians don't validate oral comments. Not in the way I think you mean. The best they can do is compare multiple sources and come up with a muddled consensus. Even the respected sources (Plutarch, Bede, etc.) were still citizens of their time, vulnerable to biases and politics, dependent on one-sided oral histories or sometimes the written accounts taken down by other historians--historians who were also dependent on oral histories.

The same is still true with more modern history. George Washington probably didn't cut down a cherry tree. Al Gore never said he invented the internet.

History is a tall-tale we all try to agree on. Never let anyone tell you otherwise.