Yes they have written a backstory he was born in California and lives there
Not true.
They've said that the character is a blank slate. Their only real history seems to be that they're delivering a package to Primm from California. Where they're originally from, and everything else about them is up in the air.
Also, the Courier doesn't have amnesia.
Have they ever actually said that he/she is from California? Or only that they are delivering the package from there to Primm?
Talonfire is correct. Sawyer said that the only set thing in the Courier's past is that he is delivering a package from California to Primm. How he got to California, what he did before, why he decided to take a courier job, where he was born, when he was born, etc. are all unwritten so that the player can create their own backstory. New Vegas will probably have the most opportunity of any Fallout game for defining your character's past in any way you see fit.