Position: Privacy in Personalized AI Is a System Property, Not Just a Model Property

In personalized AI applications, such as conversational assistants and recommender systems, users interact not with models in isolation but with broader systems that access, infer, and reuse user information across components and over time. While such use of user information is integral to personalization, it also raises important privacy questions. In this paper, we argue that individual model- or component-level analyses may not capture all privacy risks arising in such systems, motivating a system-level perspective on privacy. We distinguish and analyze four interconnected privacy-risk channels in personalized AI, and subsequently propose four requirements for system-level privacy evaluation, covering interaction trajectories, internal information flows, indirect leakage, and the privacy-utility trade-off. We argue for their systematic incorporation into privacy audits of personalized AI.