D-4h-symmetric molecules, typified by metalloporphyrins and their symmetric derivatives, generally have allowed optical transitions to a pair of degenerate electronic states. Should emission from these states display little or no splitting, one may postulate that static Jahn-Teller effects are unimportant and that the states remain essentially degenerate during relaxation. We show that the quantum mechanics and stochastic kinetics of such 'rigorously square' systems require degeneracy between two relaxation rates that have previously been assumed distinct from one another. We discuss the need for reinterpretation of certain time-resolved anisotropy data and explore the resolution of some dilemmas arising.