Machine-learned interatomic potentials (MLIPs) now rival density functional theory in accuracy and are increasingly used to screen vast crystal databases, yet they can produce unreliable predictions for chemistries outside their training distribution without clear warning. Existing force-level evidential approaches do not inherently define a corresponding uncertainty model over the potential energy surface, limiting the consistent propagation of uncertainty to energy-derived observables. Here we introduce Energy-Propagated Intrinsic Confidence (EPIC), a general energy-centered evidential framework that derives forces as exact gradients of the predicted mean energy, ensuring conservative force fields while providing an analytical estimate of energy uncertainty. Coupled to a MACE backbone trained on the Materials Project trajectory dataset, EPIC propagates uncertainty diagnostics to equations of state, anisotropic structural uncertainty ellipsoids, and phonon dispersions through a Monte Carlo procedure. Applied to 10,966 candidate crystals, the fraction classified as robustly dynamically stable increases from 11% in the highest-uncertainty quartile to 53% in the lowest-uncertainty quartile. Furthermore, element-resolved analysis reveals a pronounced chemistry dependence in the relationship between epistemic uncertainty and predicted dynamical stability, highlighting potential limitations in the description of complex bonding environments. EPIC thus provides a physics-aware, chemistry-sensitive uncertainty diagnostic for high-throughput screening and autonomous materials discovery.