We introduce a framework that uses simulation-based calibration to assess data contribution in multi-source inference, systematically evaluating what each data source contributes to parameter estimation. When inference is fast enough, calibration becomes a practical diagnostic tool. We demonstrate the framework using Bayesian optimization likelihood-free inference (BOLFI) applied to a target cell limited model of influenza A virus dynamics, combining RNA measurements and endpoint dilution assay data from single-cycle and multiple-cycle experiments. BOLFI achieves a 20-fold speed-up over traditional MCMC and requires no likelihood knowledge. A Gaussian process classifier handles simulation failures, and a discrepancy design integrates heterogeneous data types. The results reveal a counter-intuitive finding: combining all data sources does not always improve inference. The single-cycle experiment alone is most reliable for the virion entry rate, while ED-only data is best for the total RNA production rate. ED data improves calibration of the infectious virion production rate and the infectious phase duration when combined with RNA data. For the eclipse phase duration, the multiple-cycle experiment alone is more reliable, indicating that adding single-cycle data introduces inconsistency. This reveals a trade-off between precision and calibration. Based on these findings, we explore a composite diagnostic that selects the best-calibrated data type for each parameter, serving as a sensitivity check. The inference also reveals a 35-fold disparity between RNA and infectious virus production. This work demonstrates that computational efficiency enables a new level of methodological rigor: systematic calibration-guided data fusion. The framework is general and applicable to other multi-source inference problems where simulation-based models are used.

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