Chance-constrained Model Predictive Path Integral (MPPI) control is increasingly adopted for navigation in dynamic environments to explicitly bound collision risk. However, these probabilistic guarantees implicitly assume that upstream uncertainties from localization and perception are well-calibrated. In practice, estimators are often miscalibrated, inducing characteristic closed-loop failure modes: overconfidence leads to systematic safety violations, while underconfidence triggers overly conservative freezing or probability dilution. To address this critical gap, our primary contribution is a rigorous evaluation methodology applying proper scoring rules to assess the statistical validity of predicted collision risks during closed-loop execution. Concurrently, Dual-Uncertainty Chance-Constrained Tube MPPI (DUCCT-MPPI) is proposed as a real-time, risk-aware planning architecture. DUCCT-MPPI jointly integrates localization uncertainty via a one-tube Unscented Transform (UT) approximation and dynamic obstacle prediction uncertainty via Monte Carlo aggregation. Through extensive physics-based simulations, the framework demonstrates robust failure-mitigation, seamlessly transitioning to safe, conservative maneuvering without succumbing to functional deadlocks in highly cluttered environments. In highly cluttered environments, DUCCT-MPPI achieves superior robustness, outperforming established Monte Carlo MPPI baselines by nearly 28\% in navigation success rate, while simultaneously recording the lowest travel times and minimizing induced social forces. Ultimately, these findings establish that reliable probabilistic safety in autonomous navigation dictates not only expressive risk models but statistically valid uncertainty estimates throughout the entire autonomy stack.
