Here’s the deal from my “don’t have a clue” viewpoint:

The “unemployment rate” is no more and no less than what the Bureau of Labor Statistics says it is. That’s because BLS is the keeper and collector of the data. If you study its incredibly data-rich web site at bls.gov, you will see it maintains numerous different statistics relating to employment and unemployment and is well aware of the limitations and contours of each. No one statistic can give a full picture of this complex reality.

For some long-term perspective, go to this page and select 1948 for starting date: http://data.bls.gov/PDQ/servlet/SurveyOutputServlet. Bad as it is now, it is still not bad for a recession, historically speaking.

You are certainly correct that the official rate does not count people who say they are not looking for work. That is as it must be, because some people who are not looking might be able to find work if they looked.

Information on these “discouraged workers” is available, however. See http://www.bls.gov/webapps/legacy/cpsatab13.htm, where you can generate various charts of historical data specifically addressing them. This limitation of the measure leads to the paradox of “unemployment” going up a bit as the economy recovers, because these people begin looking for work again at a higher rate than the jobs recovery can absorb them.