A desert is defined as an area that receives less than 10 inches of precipitation per year. Deserts are classified by their dryness or aridity.
Semi-arid (least dry), arid (dry), and hyper-arid (driest)
I believe the Dehesa area would be considered desert.
http://library.thinkquest.org/26634/desert/intro.htm
http://www.worldclimate.com/worldclimate/cgi-bin/grid.pl?gr=N33W117
I understand what you are saying, and agree sometimes San Diego is called a desert, rainfall is close to 10 inches, Poway & Escondido around 12 inches, but many characteristics do not exist, thus my calling it not a "true desert". Areas such as Las Vegas and Phoenix once vaste wastelands have become cooler and more temperate by irrigation, and transplanted plants, swimming pools etc. Areas of So Cal are the same and should the imported water stop, they would return to their former selves.