We show that the recently-introduced formalism by Neuhauser et al. for the calculation of the quasi-particle energies of electronic systems within the framework of the GW approximation of the self-energy operator, named the `stochastic GW approach and empirically shown to have a linear-scaling arithmetic complexity for increasing number of electrons, suffers from two fundamental shortcomings that cannot be overcome while maintaining the present empirical linear-scaling property of the approach.