You might not have been. In Morrowind even if you were a Dark Elf you were summarily informed that you did not hail from Morrowind, no matter how much you wanted to
I'm pretty sure that when I started roleplaying my Nord I was born in the mountains bordering Cyrodiil. I was on a hunting trip when I got captured by those bastards and wheeled in to Helgen.
EDIT: They should've considered putting in a variety of race-specific speech cues, so that people playing different races get a more unique experience. I'm not claiming that the game is entirely void of this, but as I said above, race emmersion seems extremely overlooked.