Collapse-based models for gravity do not violate the entanglement-based witness of non-classicality

It is known that an entanglement-based witness of non-classicality can be applied to testing quantum effects in gravity. Specifically, if a system can create entanglement between two quantum probes by local means only, then it must be non-classical. Recently, claims have been made that collapse-based models of classical gravity, i.e. Di\'osi-Penrose model, can predict gravitationally induced entanglement between quantum objects, resulting in gravitationally induced entanglement is insufficient to conclude that gravity is fundamentally quantum, contrary to the witness statement. Here we vindicate the witness. We analyze the underlying physics of collapse-based models for gravity and show that these models have nonlocal features, violating the principle of locality.