As a former rehab nurse I can tell you that if you are taking a drug test, for employment, workers' compensation, court order that when you sign the paper work to have it done you are also giving up your privacy. The policy varies from lab to lab. The past 7 years I have been working as a medical investigator and this issue came up once before in MI for the company I worked for and every time the state and other states have backed up the labs for supervising UA's.

You can refuse to have supervision, but then the lab will throw the specimen out and report it to who ever requested the drug test.