In the first example of the doctor purposely killing his patients a statistician would say this doctor fit the statistically predicted outcome. But what isn't discussed is that this doctor must have existed as an anomaly within his career group. He had to have been ABNORMALLY excellent as a doctor, it is the only way he could hide his victims within his normal morbidity rates.
This is one of the reasons anomaly detection is such an interesting field because it requires dimensional understanding of a subject.