Calculations have been presented for the intermediate scattering function, dynamic structure factor, and dynamic susceptibility of a complex correlated system undergoing relaxation with independent vibrations. The vibrational contribution was approximated by a Debye spectrum, smoothed at high frequency, while the coupling model was used to describe the relaxation. This model asserts for nonpolymeric glass-forming liquids a crossover at a microscopic time from intermolecularly uncorrelated relaxation at a constant rate to intermolecularly coupled relaxation with a time-dependent, slowed-down rate. Although the model has previously been employed to successfully predict and otherwise account for a number of macroscopic relaxation phenomena, critical phenomena are not included in, and cannot be addressed by, the coupling model. Notwithstanding an absence of any change in transport mechanism for the supercooled liquid at a critical temperature, the coupling model data, when analyzed in the manner used for mode coupling theory, shows various features interpreted by MCT as critical dynamic singularities. These include an apparent fast "beta" relaxation giving rise to a cusp in the temperature dependence of the Debye-Waller factor, a power-law divergence in the temperature dependence of the relaxation time for the a process, and critical exponents for the relaxation having a defined relationship to one another. Additionally, other experimental features of the short-time dynamics, such as the anomalous Debye-Waller factor and the von Schweidler law, are also observed in results derived from the coupling model. Whatever similarities underlie the coupling model and MCT, a crucial difference is that only the latter predicts the existence of critical phenomena. Yet these and other distinct features are exhibited by the coupling model data. Evidently, any interpretation of short-time behavior in terms of MCT is ambiguous, if not necessarily incorrect. This indicates the importance of the many macroscopic-time relaxation properties found over the years in glass forming liquids (including polymers, small molecule van der Waal liquids, and inorganic materials), and the necessity that they be addressed by any theory, including MCT, purporting to offer a fundamental description of relaxation phenomena.