To get back on topic to the original question in this thread,
How exactly did the Hero Medal become the artifact that symbolizes the one meant to beat Magus?
I would start with the most likely OoC answer. The developers probably wrote in the concept of the Hero's Medal to augment the "epic" dimension of the whole Masamune story, a basic retelling of the battle of good versus evil symbolized by the conflict between Guardia and its noble king and heroes, and the Mystics, led by Magus and his vile generals. Placing a legendary sword from bygone times of forgotten glory in the hands of an unassuming hero of virtue deep tends to be a winning strategy for the good guys, and the Hero Medal authenticates the wielder of the sword. That's how you build a legend...with little bits and pieces of validation and embellishment organized around a central idea.
However, the IC answer is elusive. How the devil
did that medal come to be associated with Magus, if Magus himself didn't exist in history prior to the Middle Ages? The same question applies to the "Magus-slaying" Masamune, too, which came up in another thread but never got answered satisfactorily. And to make matters more complicated still, any IC answer has to reflect the OoC intention. That's a tall order!
My own pet answer is that there are still more Chrono series adventures lurking behind the scenes, but that's as much a cop-out as saying "the Entity did it" when something anomalous happens. We have to make do with the facts we've got, rather than speculate outside of them.
We know that "Magus" never existed in ancient times. He showed up on the scene a few decades before the events of the game. At no time did the dialogue of Middle Ages townspeople suggest that Magus represented a more general, inheritable evil...meaning that the threat of Magus was of Magus' own making. And...crap. My computer is about to crash.