I don't think the doctor would have to explain why it was done or who called, blah, blah. (I was a nurse for 16 years) It's becoming more and more common for Obstetricians to do random drug screens. If it's negative, it's likely the patient will never even know the test was even done. If it's positive, I don't think the emphasis is going to be on WHY it was done, it's going to be on the fact that it's positive and that this baby is going to need immediate and out of the ordinary personnel and medical treatment as soon as it's born. If she tests positive, she likely won't see it this way at the time, but she should be eternally grateful (if cares about this child at all-- say what you want, but being a drug addict doesn't mean that she doesn't care about her child. She is sick and needs help.) If she tests positive ahead of time, there will be protocols and procedures set up in advance to help this baby.
A urine sample is collected at every OB visit. (I'm a nurse and I have 5 children). It's not invasive and it's pretty simple to do a dip stick U/A drug analysis. I would love to see this woman raise hell about somebody calling her doctor out of concern for this baby, if she does test positive.