We use the MG treebank of Torr (2017) to investigate the conjecture in Graf (2020) that category systems are ISL-2 inferrable. A category system is ISL-2 inferrable iff the category feature of every lexical item can be jointly inferred from phonological exponents of both the item itself and either its selecting head or the arguments it selects. If correct, this conjecture would greatly limit the overgeneration problem posed by subcategorization mechanisms. Our corpus study finds that the conjecture is largely borne out, with only a few exceptions attested in the corpus. However, we also observe that it holds even for features that aren't expected to be inferrable in this manner, and we demonstrate that inferrability can arise merely from language datasets displaying Zipfian distributions. We conclude that category systems in natural languages may well be ISL-2 inferrable, but that this could be due to extragrammatical factors.