How do we know when someone knows us? Does it matter whether the knower is a human or a machine? Following the theory of interpersonal knowledge, a between-subjects experiment investigated whether a doctor’s incorporation of individualized knowledge about a patient’s social or medical history enhances doctor-patient relationships in online conversations. Patients in this study conversed with either a human doctor, an AI doctor, or an AI-assisted human doctor. Following previous research, additional factors such as perceptions of effort, relational closeness, privacy intrusiveness, and the provision of privacy control were assessed. Results showed that an AI doctor enhanced patient satisfaction when it employed social individuation messages, which triggered perceptions of increased effort, but only when patients could activate privacy control. Perception of relational closeness with a human doctor and an AI-assisted human doctor did not seem to require social individuation and privacy control. The study concludes with implications for the theory of interpersonal knowledge and AI-mediated communication research, as well as practical implications for improving chatbot medical systems.