The PBR theorem argues that if the quantum state is purely epistemic, then different preparation procedures can correspond to overlapping probability distributions over underlying states, which creates ambiguity about which preparation was used based only on observed statistics. In contrast, if the quantum state is ontic, distinct quantum states correspond to non-overlapping distributions, so in principle one can always infer the preparation given sufficient data. The theorem shows that any model with such overlap cannot reproduce all quantum predictions, and therefore concludes that the quantum state must be ontic.

However, this conclusion relies on the assumption of preparation independence, meaning that independently prepared systems have independent underlying states. If this assumption is relaxed and underlying states can depend on the joint preparation context, then overlap need not occur even in models that are otherwise epistemic. See this paper for example: https://arxiv.org/pdf/1811.01107. In this sense, such models may still be called psi-ontic under PBR’s definition, since distinct wavefunctions correspond to distinct underlying states, but the distinction reflects differences in preparation conditions rather than the existence of distinct physical wave-like entities.

Related work has pointed out that PBR’s criterion can classify intuitively epistemic models as ontic when preparation independence is violated, as discussed in this paper: https://arxiv.org/pdf/2109.02676v2. Other results show more explicitly that by dropping this assumption, one can construct models consistent with quantum mechanics in which different quantum states correspond to the same underlying reality, allowing genuine overlap, as in this paper: https://arxiv.org/pdf/1201.6554.

You should check out this lecture: https://pirsa.org/12050021