Step 1: Understanding the Question.
This is a case control study looking at whether the contraceptive pill is linked to breast cancer. We need to find the ONE statement about control selection or risk measurement that is NOT true.
Step 2: Key Concept.
In a case control study, cases (women with breast cancer) and controls (women without breast cancer) are picked first, and their past exposure to the pill is then compared. Because the disease status is fixed by design, a case control study can only give an odds ratio, which is a fair stand in for relative risk when the disease is rare. It cannot give the actual incidence rate in exposed and unexposed groups, so it cannot give attributable risk directly.
Step 3: Detailed Explanation.
Option (A) is a basic rule of control selection: controls must be drawn from the same source population as cases, so they carry the same background chance of getting breast cancer. This is true.
Option (B) is also sound practice: excluding women who are currently on the pill from the control group keeps the comparison of past exposure clean and avoids mixing up timing of exposure. This is true.
Option (C) reflects that controls are meant to be disease free at the time of selection, so restricting them to healthy women (free of breast cancer) is standard. This is true.
Option (D) claims that attributable risk, meaning the actual extra risk of breast cancer caused by the pill, can be worked out directly. Attributable risk needs the incidence of disease in exposed and unexposed groups, and a case control study never measures incidence because the number of cases and controls is fixed by the researcher, not by natural disease occurrence. So attributable risk cannot be measured directly in this design, only estimated indirectly using the odds ratio and background incidence from another source. This statement is false.
Step 4: Final Answer.
The false statement is that attributable risk may be directly measured, since a case control study only yields relative risk (odds ratio), not attributable risk.
\[ \boxed{\text{The attributable risk of breast cancer resulting from the pill may be directly measured}} \]