Vehicle-bridge coupling (VBC) models of passing vehicle problems are inherently nonlinear due to the existence of the VBC term. To obtain analytical solutions, this term is often neglected. However, such neglect may lead to significant errors, particularly when the vehicle mass is larger. To further investigate the impact of neglecting the VBC term, one can treat it as a generalized Eshelby-force, which is solely a function of the bridge response. With this understanding, several numerical simulations are presented in this paper. Compared to conventional methods, the proposed model exhibits markedly improved alignment with finite element (FE) results. In terms of bridge condition assessment, the VBC term primarily affects the first-order amplitude in frequency and mode identification, as well as the equivalent acceleration amplitude in passive tap-scan damage detection. Since these factors do not compromise the accuracy of the original methods, the challenge associated with the VBC term is not considered a hindrance to the accuracy of bridge condition assessment methods. All these findings provide significant insights for our understanding of the passing vehicle problems.