Origin-destination (OD) flow prediction remains a core task in GIS and urban analytics, yet practical deployments face two conflicting needs: high accuracy and clear interpretability. This paper develops AMBIT, a gray-box framework that augments physical mobility baselines with interpretable tree models. We begin with a comprehensive audit of classical spatial interaction models on a year-long, hourly NYC taxi OD dataset. The audit shows that most physical models are fragile at this temporal resolution; PPML gravity is the strongest physical baseline, while constrained variants improve when calibrated on full OD margins but remain notably weaker. We then build residual learners on top of physical baselines using gradient-boosted trees and SHAP analysis, demonstrating that (i) physics-grounded residuals approach the accuracy of a strong tree-based predictor while retaining interpretable structure, and (ii) POI-anchored residuals are consistently competitive and most robust under spatial generalization. We provide a reproducible pipeline, rich diagnostics, and spatial error analysis designed for urban decision-making.