Traditional tunes

So I am back home in Scotland, and in trying to think of a suitable Scottish subject was reminded of the claim occasionally encountered that the song 'Scots Wha Hae' dates from the battle of Bannockburn (1314), suggesting it would be highly suitable for us to include in our repertoire.

In fact, it is reasonably well known that the words were written by Robert Burns in 1793, imagining the words of a rousing speech by Robert the Bruce before the battle. But you can find everywhere claim that the tune "according to tradition, was played by Bruce's army at the Battle of Bannockburn, and by the Franco-Scots army at the Siege of Orleans" (Wikipedia).

However, the tune is stylistically so different from anything surviving from the middle ages that this seems vanishingly improbable; indeed it seems most likely to date from not long before the earliest known versions which have Jacobite words (i.e., early 18th century). I've never quite understood why people sometimes seem to think that 'traditional' means there was no origin, or at least, that this designation is sufficient to justify including a tune (or some other traditional activity) in a medieval event.