As far as I know, all pilots are very very serious about their tasks and responsibilities when it comes to work. The fact that we should be subject to random screening is in it self an assumtion that there is a need for it.
As mentioned before, I felt great discomfort with having to undergo the tests, even though I know I have nothing to hide. In my pervious life I conducted alcohol and drugs tests on military personell, and I know that there is a margin of error.
As you said, if an error does occur, the person affected will be subject to even more suspicion.
We have a peer intervention culture that workes well, and in addition we have to do a medical examination once or twice a year. The doctors will pick up any hits of alcoholism. And if the person is not a drunk, than I trust my peers judgement. And trust them not to show up for work if in doubt of the alcohol, or drug level in their blood.
The same judgement I trust them to use when operating heavy metal at high speeds!!