Of course they don't drink their own urine in that state! Of course it has been done by people in order to stay alive during unusual situations. It won't kill you if you did, just not exactly something that you would want to do.
.
Urine is a waste product of the body which needs to be filtered to remove the harmful nitrogen products it contains if you intend to drink it. Sergeant_ Torpedo suggested filtering it through sand in this thread:
http://www.lpsg.org/644590-post10.html
In the dying of thirst situation you are only after the liquid water, all the other wastes need to be removed. Usually when in a thirsting situation the body concentrates the urine as much as possible so there is probably very little recoverable water in the urine of a thirsting person.
Urine is also an ideal growth medium for bacteria. Therefore its best to filter it while it is fresh.
http://www.lpsg.org/644559-post4.html