Board Thread:Oblivion/@comment-9716469-20130519212835/@comment-6881629-20130520162342

Maybe it was somehow enchanted by Akatosh when he created it to only recognize a Septim or being a desendant leave a small diluted amount of dragon blood (though the lore would say no) and that lets the wear the amulet.

A actual Dragonborn has the blood and soul of a dragon its a rare blessing from Akatosh not something that is fully passed down to another generation. As the Dragonborn page says (copy/paste) -

"The first Dragonborn was purportedly Saint Alessia, the Nedic slave queen who was blessed by Akatosh and given the Amulet of Kings to seal the covenant between them. This began the tradition of all legitimate rulers of the Cyrodilic Empire referred to as Dragonborn as only they could wear the Amulet of Kings and light the Dragonfires..."

"Dragonborn scarcely exist, and it is rare for more than one to appear within an era. They can belong to any race or gender, since the Dragon blood is a "gift" bestowed to certain mortals favored by Akatosh."

Septims are all referred to as Dragonborn as a title not as a actual Dragonborn (like Alessia, Tiber Septim, the player or Miraak). Thats the way i interpret it anyway.