Real-world image dehazing (RID) aims to remove haze-induced degradation from real scenes. This task remains challenging due to non-uniform haze distribution, spatially varying color shifts, and the scarcity of paired real hazy-clean data. In PRISM, we propose Proximal Scattering Atmosphere Reconstruction (PSAR), a physically structured framework that jointly reconstructs the clear scene and scattering variables under the atmospheric scattering model, making the restoration process more interpretable in complex real-world conditions. To bridge the synthetic-to-real gap, we design an online non-uniform haze synthesis pipeline and a Selective Self-Distillation Adaptation (SSDA) scheme for unpaired real-world scenarios, which enables the model to selectively learn from high-quality perceptual targets while leveraging its intrinsic scattering understanding to audit residual haze and guide self-refinement. Experiments on real-world benchmarks demonstrate that PRISM achieves competitive performance on RID tasks.