As others have said, whether or not a sword will shatter depends more on its own material properties than on the quality of the sword it is striking. However, there is at least one way in which your Amazing Swords might cause other swords to shatter much more often than they would normally - if it were otherwise rare for swords to contact each other directly.
As a target, all swords, from the worst to the best, present a similar challenge to the attacking sword. Flesh, bone, or a wooden shield present a lesser (though still not negligible) challenge. In any impact some of the energy is dissipated as the sword cuts into the target, the interaction time is lengthened and the instantaneous force applied to the sword is reduced. If normal swords in your setting were consistently mediocre, then they might rarely shatter against shields but quite routinely shatter against each other.
Dominant fighting styles would heavily emphasize the use of the shield, both in defending against incoming attacks and in creating openings for your own attacks. Parrying or making an attack that is parried reduces the combat to a coin-toss - either your sword will break or your opponent's will. 523
Worse, even if you survive, your sword is probably now chipped and much more likely to shatter in the next encounter, perhaps even against a shield.
Now high quality Amazing Swords appear and their wielders fight in a new style. Incoming attacks are forcefully parried. Their own attacks are made to try to force a parry from their opponent. If the opponent's sword doesn't shatter on the first collision then the attacks keep coming until the chips become fractures.
One problem with this approach is in getting your ordinary swords to be reliably, consistently mediocre. My first instinct for how to achieve this would be to couple poor quality ores with a highly ritualised process of refinement and manufacture. Due to the poor quality ores, most deviations from the normal process lead to total failure. Swords that don't immediately shatter when drawn are rationalised as the result of appeasing the god(s)/spirits/ancestors by following the ritual, and so the ritual is followed closely. 523