The adsorption of hard-sphere gas in a random porous media and/or in a disordered hard sphere matrix is studied by applying the replica-Ornstein-Zernike (ROZ) equations for the quenched-annealed systems. Our interests are (1) to derive new formulas for the chemical potentials and the potential distributions theorems for such systems and (2) to use these derivations as consistency requirements for improving the closure relations in the ROZ. Two types of consistencies are enforced: (i) bulk thermodynamic property consistencies, such as the Gibbs-Duhem relation and (ii) zero-separation theorems on the cavity functions. Five hard-sphere matrix/hard-sphere fluid systems have been investigated, representing different porosities and size ratios. Direct formulas for the chemical potentials and the zero-separation theorems for the fluid cavity functions are derived and tested. We find uniformly better agreement with Monte Carlo data when self-consistency is enforced, than the conventional closures: such as the Percus-Yevick and hypernetted chain equations. In general, the structural properties are improved, as well as the thermodynamic properties. There remains discrepancy in the fluid-replica structure h(12)(r) at coincidence, r=0. The nature of the h(12)(r) behavior is discussed in light of the consistency principles.