The study of geometrically frustrated magnets with unusual crystal field ground states offers the possibility of discovering new aspects of the physics of cooperative paramagnetic states. In the rare-earth double perovskite Ba2HoSbO6 the Ho3+ ions occupy a face-centered cubic lattice, which frustrates near-neighbor antiferromagnetic coupling. We present a systematic experimental study of the system using dc magnetization, heat capacity, muon-spin relaxation, inelastic neutron scattering, neutron powder diffraction, and neutron polarization analysis. The bulk measurements at first point to spin liquid behavior, but the microscopic measurements indicate that this system is an example of a “nonmagnetic doublet” crystal field ground state, with low-lying excited states. Our measurements are interpreted using crystal field theory of Ho3+, including hyperfine coupling. We find that exchange and dipolar coupling are weak in this particular system and that the “mock spin liquid” behavior in fact reflects the unusual properties of the nonmagnetic doublet.