I have had to give witnessed urine samples more than I would care for being in the profession I am in, and I have also had them done where I was given a bit of privacy too. I much prefer them that way, as in with privacy, than without.
At one of the jobs I worked, an entire emergency drug box came up missing on Easter morning actually. Had a value of about 60,000 dollars on the street so I was told. Needless to say, it was a huge deal. The state was notified who in turn decided it was too big for them to handle so the FBI was called in to complete the investigation.
Everyone who was working the day before, the day of, and the day after Easter was tested. According to my friends who were tested, women tested women, and men tested men, all were witnessed. The women had to drop their pants so that the agent could visably see the urine stream flowing into the cup. All I can say is I was very thankful I was at my parents house during that time in question. I was questioned as to who I thought would do something like that, and that was nerve wracking enough, trust me.
I also have another nurse friend who was mandated for drug testing by the state who also had to be witnessed in the same way the FBI did, but depending on what day she was selected, she would have to do so in front of both sexes. She said after the first few times, it didn't really matter much. They were both nurses and they had both seen it all before.