When dealing with modal representations of the Green's function of a complex medium, the modal coefficients are often assimilated to random variables, where statistical independence is justified on heuristic arguments supported by the complexity of the propagation in multiple-scattering scenarios. This letter addresses this assumption when the randomness originates from an uncertain positioning of the sources, proving under what conditions the modal coefficients can be regarded as uncorrelated, showing that this special condition should not be taken for granted, even in complex media.