An exact analysis of coupled coherent state (CCS) theory in the moving locally quadratic Hamiltonian approximation is shown to reproduce both the linearized coherent state matrix element of the Herman-Kluk propagator and the coherent state overlap with Heller's thawed Gaussian wave function. The derivation is applicable to anharmonic as well as harmonic systems, because the quadratic approximation is taken to apply only in the vicinity of a particular classical trajectory. New compact expressions for the linearized Herman-Kluk coherent state matrix element are given, and improvements for the practical application of CCS theory are discussed. (C) 2003 American Institute of Physics.