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Offloading data traffic from Infrastructure-to-Device (I2D) to Device-to-Device (D2D) communications is a powerful tool for reducing congestion, energy consumption, and spectrum usage of mobile cellular networks. Prior network-level studies on D2D data offloading focus on high level performance metrics as the offloading efficiency, and take into account the radio propagation aspects by using simplistic wireless channel models. We consider a D2D data offloading protocol tailored to highly dynamic scenarios as vehicular environments, and evaluate its performance focusing on physical layer aspects, like energy consumption and spectral efficiency. We do this by taking into account more realistic models of the wireless channel, with respect to the simplistic ones generally used in the previous studies. Our objective is twofold: first, to quantify the performance gain of the considered D2D offloading protocol with respect to a classic cellular network, based on I2D communications, in terms of energy consumption and spectral efficiency. Second, to show that using simplistic channel models may prevent to accurately evaluate the performance gain. Additionally, the use of more elaborated models allows to obtain insightful information on relevant system-level parameters settings, which would not be possible to obtain by using simple models. The considered channel models have been proposed and validated, in the recent years, through large-scale measurements campaigns. Our results show that the considered protocol is able to achieve a reduction in the energy consumption of up to 35%, and an increase in the system spectral efficiency of 50%, with respect to the benchmark cellular system. The use of different channel models in evaluating these metrics may result, in the worst case, in a sixfold underestimation of the achieved improvement.