In this paper we investigate how randomness in biochemical network dynamics improves identification of the network structure. Focusing on the case of so-called population snapshot data, we set out the problem as that of reconstructing the unknown stoichiometry matrix and rate parameters of the network in the case of state-affine reaction rates. We discuss what additional information is conveyed by the observation of second-order moments of the system species relative to the sole knowledge of their mean profiles. We then illustrate the impact of this additional piece of information in the reconstruction of an unknown network structure by means of a simple numerical example.