This recent KCET article by Carren Jao clears it up.

To celebrate the 231st birthday of the city of Los Angeles the LA Times is prepared a little investigation about the oldest building in Los Angeles.

Another version of this article appears on the Huffington Post too.

LA Now produced this short segment showing some great interior and exterior shots of the structure.

Sanchez Adobe from Mark Ridley-Thomas on Vimeo.