The dragonborn template is poorly written. I think what they meant for it to do was that you keep your type, and gain the dragonborn subtype. But the authors just assumed that everyone taking it would have the humanoid type, and wrote half the description as if that were true.
So if you were an Outsider (Native), you'd just add the (Dragonblood) subtype. You'd keep Darkvision and all of the other things you gain strictly because of your Outsider type, but lose any racial specific things like the Aasimar's Light ability (IIRC, I don't remember exactly what you keep/lose as a Dragonborn).
Again, this is just my interpretation. The template as written is pretty much unusable for non-humanoids, as it is self-contradictory.