While elongated particles in viscous fluids follow Jeffery orbits, their dynamics in dense granular flows remain unresolved. We demonstrate that sheared, low friction granular rods do not follow these orbits, but instead reach a quasi-equilibrium state quantitatively described by classical liquid crystal theory, with collisions providing effective thermal noise. This quasi-equilibrium analogy breaks down at two limits: low aspect ratios, where the theory incorrectly predicts isotropy, and high inter-particle friction, which drives a transition from steric screening to frictional gearing. We map this far-from-equilibrium breakdown using a phenomenological effective Ericksen number, establishing the limits of thermal thermodynamic analogies in driven athermal matter.