Hybrid mechanistic-statistical models offer interpretability and adaptability for short-term seasonal epidemic forecasting, but it remains unclear whether their accuracy depends more on increased biological complexity or on the assimilation of richer data. Using eight retrospective influenza seasons in North Carolina, we evaluate whether training on historical data and assimilating auxiliary emergency department (ED) visit data improves four-week-ahead hospital admission forecasts more than adding biological complexity (multi-subtype structure and cross-season immunity). Hierarchical Bayesian training on historical data improves accuracy by 22.4 % (95 % CI: 16.4-28.1 %), and inclusion of ED visit data yields a further 5.3 % (95 % CI: 3.0-7.6 %) improvement, whereas added biological complexity produces diminishing or null gains. We further observe a substitution effect in which ED visit data partially compensates for omitted biological structure. We deployed a simplified model variant in the 2025-2026 CDC FluSight Challenge and ranked among the top ensemble performers, supporting the robustness of Bayesian hierarchical training in real time. Together, these findings indicate that short-term forecast accuracy is driven more by historical learning and assimilating auxiliary signals than by biological fidelity, with implications for how forecasting systems should balance mechanistic complexity.