Gravity-induced entanglement (GIE) experiments have been proposed as a theory-independent test of the quantum nature of gravity, on the strength of several no-go theorems concluding that GIE detection implies the gravitational interaction is either nonlocal or nonclassical. This is in apparent tension with a growing number of papers claiming that theories with a classical gravitational field do predict GIE. This article resolves the tension by reviewing the assumptions of the no-go theorems and highlighting the information-theoretic, rather than spatiotemporal, nature of the locality assumption. This makes violating locality not particularly problematic. Indeed, quantum electrodynamics and perturbative quantum gravity are nonlocal in the sense of the theorems. Given that GIE detection is not sufficient to rule out a classical gravitational field, the quantitative comparison of theoretical predictions in the low-energy quantum gravity regime will allow us to test whether the gravitational field is quantum or classical.