Crystallization in suspensions of colloidal hard spheres with a volume fraction of 0.631 +/- 0.004, and a polydispersity of less than 3%, is studied experimentally. The mass density of the solvent is almost equal to that of the particles. Normal (1g-like) gravity conditions are simulated by centrifugation. It is shown that there is a limiting density of the quenched hard-sphere fluid, close or equal to the random close-packed density (with a volume fraction of 0.644 +/- 0.005), above which crystallization is no longer observed. The results rule out the possibility that gravitational stress in quenched colloidal hard-sphere fluids, with volume fractions lower than the one corresponding to random close packing of spheres, irreversibly induces a packing geometry in which crystallization is suppressed.