Sorry, OP, seems like you are a bit naive in the ways of the world. A hospital needs to do those things for numerous reasons. Access to drugs is one of them, but less pertitent than access to client information. You are an IT guy, so there is almost a 100% certainty you are going to have access to client information at some point. And yes, even the IT guy needs to be trustworthy. If you worked at the CIA and were an IT guy, don't you think that they would make you take a drug test there too?
People are rightfully very concerned about medical history privacy. An abused IT position is a scary thought.
What does this have to do with drugs? Well, aside from the theory that a drug user will be more likely to do something crazy, which I'm not sure about but is out there, there's the fact that very few drugs don't cloud judgement or brain activity in some fashion, which means even if you don't intentionally make an error which compromises data, you might do it unintentionally.
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