Final answer:
The principle illustrated by allowing cancer researchers to use existing hospital data without individual patient consent is Public Responsibility, recognizing that some health information uses are critical for the public good and research.
Step-by-step explanation:
Allowing cancer researchers to use the existing data in hospital systems without asking each patient for permission illustrates the principle of Public Responsibility underlying the HIPAA privacy rule. This principle acknowledges that certain uses of health information may be so important to the public good that they outweigh individual privacy considerations.
Examples of such purposes might include research, public health activities, and health care operations where the data are essential for improving health outcomes on a broad scale. HIPAA allows for such uses provided that the data are adequately protected and that the privacy risks to individuals are minimized. For instance, data might be de-identified or used only within secure research environments.