If you watch Discovery Health, you will know, IN CALIFORNIA, they must wait 12 hours after declaring you brain dead, and before harvesting organs. It's very difficult to keep someone's organs going on life support for that period if they have bled out from a head wound or some auto accident.
Also, "they won't try to save me if I'm an organ donor" is an urban legend, a myth, it's baloney.
And having "DNR" tattooed on your chest is not sufficient to prevent the paramedics from giving CPR or defibrillating--in Texas, at least, a written, properly executed out of hospital dnr form (on the state promulgate form, no less) with proper identification is required.