Although actin and myosin are important contributors to cell-force generation, shape change, and motility, their contributions to cell stiffness and frequency-dependent rheology have not been conclusively determined. We apply several pharmacological interventions to cultured epithelial cells to elucidate the roles of actin and myosin in the mechanical response of cells and intracellular fluctuations. A suite of different methods is used to separately examine the mechanics of the deep cell interior and cortex, in response to depletion of intracellular ATP, depolymerization of F-actin, and inhibition of myosin II. Comparison of these results shows that F-actin plays a significant role in the mechanics of the cortical region of epithelial cells, but its disruption has no discernable effect on the rheology of the deeper interior. Moreover, we find that myosins do not contribute significantly to the rheology or ATP-dependent, non-Brownian motion in the cell interior. Finally, we investigate the broad distribution of apparent stiffness values reported by some microrheology methods, which are not observed with two-point microrheology. Based on our findings and a simple model, we conclude that heterogeneity of the tracer-cytoskeleton contacts, rather than the network itself, can explain the broad distribution of apparent stiffnesses.