In this investigation, equilibrium molecular dynamics simulations were conducted to assess the influence of the interface modeling approach on the calculation of hydrodynamic slip in carbon nanochannels. A Green-Kubo formalism was implemented for the calculation of the slip length in water confined by graphite layers. The nonbonded interactions between solid and liquid atoms (interface models) were modeled using parameters optimized to represent the wetting behavior and adsorption energy curves from electronic structure calculations. Conventional carbon-oxygen-only interaction models were compared against comprehensive models able to represent the molecular-orientation-dependent energy of interaction. Quasi-universal relationships built under the premise of the slip length dependence on the water-graphite affinity and characterized by macroscopic wettability were critically assessed. It was found that the wetting behavior cannot fully characterize the hydrodynamic slip because interface models that produced the same surface wettability yielded different values of the friction coefficient. Alternatively, the density depletion length, used to characterize the interfacial liquid structuring and the availability of momentum carriers (interfacial water molecules), was able to accurately represent the slip length trends independently of the interface model. These findings reassert the importance of physically sound interface models to study interfacial transport properties and the need of reliable parameters and characterization procedures to support theoretical models that seek to unveil the inconsistencies in hydrodynamic slip calculations.