The state-of-the-art high-fidelity state-to-state (StS) model is performed to investigate the hypersonic shock wave/laminar boundary layer interaction over a 25(degrees)-55(degrees) double cone. This work aims to clarify whether the shortcomings of thermochemical models are the underlying source for the discrepancies between the simulations and experiments. A high-enthalpy nitrogen flow with a Mach number of 11.54 and a unit Reynolds number of 4.394 x 10( 5)/m is considered. We first find that the StS and widely used two-temperature models yield two different shock reflection patterns (i.e., the regular reflection and Mach reflection, respectively). However, the surface pressure and heat flux distributions predicted by the two models are generally consistent, which are not influenced by the differences in the shock patterns, dissociation rates, and non-Boltzmann vibrational distributions in the flowfields. Moreover, the StS model fails to match the experiments in spite of fairly limited improvement. Our findings indicate that the shortcomings of thermochemical models are not the main reason for the discrepancies in the simulations and experiments for the high-enthalpy nitrogen double-cone flow.