Experimental joint multiplicity distributions of neutrons and charged particles provide a striking signal of the characteristic decay processes of nuclear systems following energetic nuclear reactions. They present, therefore, a valuable tool for testing theoretical models for such decay processes. The power of this experimental tool is demonstrated by a comparison of an experimental joint multiplicity distribution to the predictions of different theoretical models of statistical decay of excited nuclear systems. It is shown that, while generally phase-space based models offer a quantitative description of the observed correlation pattern of such an experimental multiplicity distribution, some models of nuclear multifragmentation fail to account for salient features of the observed correlation.