As AI systems move into operating systems, privacy no longer turns only on whether a model runs locally. A local assistant may assemble email, calendar entries, files, screenshots, notifications, and app intents; retain embeddings or summaries; invoke tools; emit telemetry; or route difficult requests to cloud infrastructure. Local inference reduces some exposure, but it answers only one question: where computation occurs. It does not answer who may assemble context, what derived state persists, which actions are authorized, or how updates change the system's authority. We develop an OS-centered privacy framework for on-device AI that treats privacy as an institutional accountability problem rather than a deployment attribute. The framework specifies a threat model, a six-part privacy risk taxonomy, privacy-by-architecture controls, and a four-level audit rubric. We demonstrate the rubric through a documentation-bounded comparison of Apple Intelligence/Foundation Models, Android AICore/Gemini Nano, and Microsoft Recall. Meaningful privacy in on-device AI depends on constrained information flow, bounded authority, visible user control, and auditable governance across the operating-system lifecycle.