Observable signatures of the quantum nature of gravity at low energies have recently emerged as a promising new research field. One prominent avenue is to test for gravitationally induced entanglement between two superposed masses. Here we analyze such proposals and what one can infer from them about the quantum nature of gravity, as well as the electromagnetic analogues of such tests. We show that it is not possible to draw conclusions about mediators: even when pre-assuming relativistic physics, the interpretation of the entanglement as generated by quantized mediators is not unique. Such indirect tests therefore have limited ability to verify that entanglement is mediated by a quantum channel, unless additional assumptions are made. As the interpretation of the experiment thus depends crucially on the assumptions one has to impose, we also show that cosmological observations already demonstrate some aspects of quantization that this experiment aims to prove. Nevertheless, the proposals would probe a new physical regime where gravity is sourced by superposed quantum states of matter.