RFID ownership transfer protocols (OTPs) transfer tag ownership rights. Recently, there has been considerable interest in such protocols, however, guaranteeing privacy for symmetric-key settings without trusted third parties (TTPs) is a challenge still unresolved. In this paper, we address this issue and show that it can be solved by using channels with positive secrecy capacity. We implement these channels with noisy tags and provide practical values, thus proving that perfect secrecy is theoretically possible. We then define a communication model that captures spatiotemporal events and describe a first example of symmetric-key based OTP that: (i) is formally secure in the proposed communication model and (ii) achieves privacy with a noisy tag wiretap channel without TTPs.