Information-theoretically secure Symmetric Private Information Retrieval (SPIR) is known to be infeasible over noiseless channels with a single server. Previous solutions involved additional resources such as database replication, shared randomness, or noisy channels. This paper demonstrates that, using a noiseless multiple access channel, SPIR with information-theoretic security guarantees is feasible without shared randomness, a noisy channel, or data replication. Specifically, we leverage a noiseless binary adder channel and employ two non-colluding servers with independent content. Furthermore, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.