Multiple explanations have been offered, and to date, they remain empirically indistinguishable in standard implementations. Here we show that one of them --the Deutsch-Hayden explanation, distinguished by its strictly local and causal flow of information --makes a concrete empirical prediction: teleportation must fail whenever the communication channel is fundamentally classical. Indeed, under the assumption that quantum information is locally mediated, we prove that if the teleportation of arbitrary unknown quantum states is successful, then the channel must be fundamentally non-classical. Our argument is quantum-information-theoretic and does not rely on the specific dynamics of systems composing the channel. This turns teleportation into a probe for the classicality of candidate communication media, making gravity a decisive test case. We thus propose a new empirical test: does gravitational communication of the two bits support a functioning teleportation protocol?