The Pusey–Barrett–Rudolph (PBR) theorem establishes \(\psi\) -onticity for individual quantum systems, but its standard formulation relies on the Preparation Independence Postulate (PIP). This has led to a prevalent view that rejecting PIP leaves open the possibility of \(\psi\) -epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes \(\psi\) -onticity for composite systems prepared in product states, the \(\psi\) -onticity of the individual subsystems follows directly from the tensor-product structure of quantum mechanics, without invoking PIP or any further auxiliary assumptions. This result removes a key auxiliary assumption from the PBR theorem, closes a persistent loophole for preserving \(\psi\) -epistemic models, and strengthens the conceptual foundations of \(\psi\) -ontology.
