P. Dupre, R. Jost, M. Lombardi, P. G. Green, E. Abramson, and R. W. Field have observed anomalous behavior of the anticrossing density in the Zeeman anticrossing (ZAC) spectra of gas phase A 1Au acetylene in the 42200 to 45300 cm-1 energy range. To best explain this result, they hypothesize a large singlet-triplet coupling due to the existence of a linear isomerization barrier connecting a triplet-excited cis- and trans-acetylene in the vicinity of the studied energy range (~45500 cm-1). Theoretically such a linear stataionary point, however, must have two different degenerate bending vibrational frequencies which are either imaginary or exactly zero. Neither case has yet been experimentally detected. Here we have studied the two lowest-lying linear triplet-excited-state stationary points of acetylene, 3Sigmau+ and 3Deltau, to see if they fit Dupre et al.'s hypothesis. We have completed geometry optimization and harmonic vibrational frequency analysis using complete-active-space self-consistent-field (CASSCF) wavefunctions as well as determined energy points at those geometries using the second-order configuration interaction (SOCI) method. Harmonic vibrational analyses of both stationary points reveal two different doubly-degenerate vibrational modes with imaginary vibrational frequencies (or negative force constants) indicating that they are indeed saddle points with a Hessian index of four. At the DZP SOCI//CASSCF level of theory with zero-point vibrational energy (ZPVE) correction, the 3Sigmau+ stationary point lies 35840 cm-1 above the ground state of acetylene. This is much too low in energy to contribute to the ZAC spectral anomaly. At the same level of theory with ZPVE correction, the 3Deltau stationary point lies 44940 cm-1 above the ground state consistent with Dupre et al.'s hypothesis. Several solutions to the anomalous ZAC spectra are discussed. We propose that the anomaly may also be due to the coupling with a nearly linear structure on the T3 surface of acetylene.