Should we necessarily treat masses as localized when analysing tests of quantum gravity?

Recently proposed ``table-top tests of quantum gravity'' involve creating, separating and recombining superpositions of masses at non-relativistic speeds. The general expectation is that these generate superpositions of gravitational fields via the Newtonian potential. Analyses suggest that negligible gravitational radiation is generated if the interference experiments involve sufficiently small accelerations. One way of thinking about this is that matter and the static gravitational field are temporarily entangled and then disentangled. Another is that the static gravitational field degrees of freedom are dependent on the matter and do not belong to a separate Hilbert space, and that there is always negligible entanglement between matter and dynamical gravitational degrees of freedom. In this last picture, localized masses effectively become infinitely extended objects, inseparable from their Newtonian potentials. While this picture seems hard to extend to a fully relativistic theory of non-quantum gravity, it has significant implications for analyses of how or whether BMV and other non-relativistic experiments might test the quantum nature of gravity. If the masses in a BMV experiment are regarded as occupying overlapping regions (or indeed all of space), explaining how they become entangled does not require that their gravitational interaction involves quantum information exchange. On this view, while the experiments test gravity in a regime where quantum theory describes all relevant matter degrees of freedom, they do not necessarily test its quantum nature. It might be argued that no plausible explanation other than quantum gravity could be consistent both with these experiments and with relativity. But this relies on further theoretical assumptions and is weaker than claiming direct evidence for quantum gravitational interactions from the experiments alone.