Navigating unknown environments with a single RGB camera is challenging, as the lack of depth information prevents reliable collision-checking. While some methods use estimated depth to build collision maps, we found that depth estimates from vision foundation models are too noisy for zero-shot navigation in cluttered environments. We propose an alternative approach: instead of using noisy estimated depth for direct collision-checking, we use it as a rich context input to a learned collision model. This model predicts the distribution of minimum obstacle clearance that the robot can expect for a given control sequence. At inference, these predictions inform a risk-aware MPC planner that minimizes estimated collision risk. We proposed a joint learning pipeline that co-trains the collision model and risk metric using both safe and unsafe trajectories. Crucially, our joint-training ensures well calibrated uncertainty in our collision model that improves navigation in highly cluttered environments. Consequently, real-world experiments show reductions in collision-rate and improvements in goal reaching and speed over several strong baselines.