The observation of long-lived electronic quantum coherence in a photosynthetic light harvesting system [Engel et al. Nature 2007, 446, 782] has led to much effort being devoted to elucidation of the quantum mechanisms of the photosynthetic excitation energy transfer. In this paper we examine the question of whether the decay of the coherent beating signal is due to quantum mechanical decoherence or ensemble dephasing (also called "fake decoherence"). We compare results based on the quantum master equation description of the time-evolution of the reduced density matrix with a mixed quantum/classical approach where the ensemble average is calculated after the dynamics. The two methods show good agreement with results from the quantum master equation in terms of the decay of quantum coherent oscillations when ensemble average is considered for the mixed quantum/classical approach. However, the results also demonstrate it remains possible that the quantum coherent motion is robust under individual realizations of the environment-induced fluctuations contrary to intuition obtained from the reduced density matrices, indicating that the decay of the observed quantum coherence should be understood as ensemble dephasing. Our calculations imply that coherence is a property of the pigment-protein system, not simply the preparation method of the electronic excitation.