Flowing bottom-hole pressure (FBHP) is a key quantity for the design, optimization, and surveillance of oil wells, yet its direct and continuous measurement is costly and often unavailable. Hybrids of a mechanistic pressure traverse and machine learning are established, but published studies report only that the combination outperforms its parts: which part produces the gain, and whether that gain survives a change of field, have not been quantified. This study addresses both on 1621 field records from seven published sources (1111 wells, 386 of them deviated), released with the paper. A Beggs–Brill traverse is marched from the measured wellhead pressure to the reference depth, and its output reaches a gradient-boosting model by two routes — as an input feature, and as an anchor whose residual is learned — crossed in a 2 × 2 ablation at fixed features and hyperparameters. Under leakage-safe well-level cross-validation the two routes prove largely redundant: of the 119 psia by which the hybrid improves on a data-driven baseline in root-mean-square error, 101 psia is delivered by the estimate entering as a single feature and a further 16 psia by the residual structure; the best configuration reaches R² = 0.957 and a mean relative error of 5.0%. Under leave-one-source-out validation the two routes separate: 10.3% mean relative error for the feature route against 8.9% for the anchor route. The untrained traverse itself remains at 7.7% out of source, so the learned correction is field-specific rather than universal, and the practical claim is limited accordingly.