Bruce Schneier summarizes a report that is either a very late April Fool story or proof that the sight of a white coat and stethescope induces compliant behaviour:
This is a pretty scary criminal tactic from Turkey. Burglars dress up as doctors, and ring doorbells handing out pills under some pretense or another. They’re actually powerful sedatives, and when people take them they pass out, and the burglars can ransack the house.
According to the article, when the police tried the same trick with placebos, they got an 86% compliance rate.
The linked report shows that people are nearly as likely to open the door when the caller claims to be a robber.