We test the recently developed state-specific multireference Brillouin-Wigner coupled cluster (MRBWCCSD) method against the single reference CCSD method by examining theoretically the competing X (3)Sigma(-) and (5)Sigma(-) states of the (experimentally unknown) isovalent calcium and zinc carbide diatomics (CaC, ZnC). At the CCSD level, CaC is "incorrectly" predicted to have a ground (5)Sigma(-) state; however, the MRBWCCSD treatment restores the correct state ordering, and improves significantly the energetics for both molecules. Further comparison with various single- and multireference treatments shows that the latter are absolutely necessary for obtaining meaningful results for the ground states in both molecules.