Continuum models are often used to study large finite assignment economies. However, some subtleties must be taken into account. We show that in the large finite random assignment problem without transfers, Competitive Equilibrium with vanishing income differences does not asymptotically characterize the set of efficient and envy-free random assignment profiles. This is in sharp contrast with the continuum model counterpart (Ashlagi and Shi, 2015). The problem is driven by the failure of local non-satiation inherent in no-transfer assignment.