I think they might have said something about Link being too young/weak to weild the Master Sword in The Ocarina of Time, but that wouldn't preclude some later Link from being strong enough to weild it without waiting until he's older.
Ultimately, I think Nintendo doesn't care about this stuff...I think the guys at Nintendo are more interested in recreating the feeling of The Legend of Zelda. That is, a young man/boy who starts out on this incredible adventure and rises from nobody to hero. The story is a nice way to frame that, and there are certain legendary elements (the Princess, the Triforce, and Ganon) that figure into most of the plots, but the series is more about adventuring and exploring than story.
That's something about videogames that I feel is being lost: this is not the same medium as television or movies, so why is it that so many game developers feel the path to making better games is to have complex plots and Hollywood voice actors? A good story is a nice bonus but it's not at the heart of the art of videogames.
Edit: typos.