The trace element compositions of Hadean zircons have been used in two ways to argue for the existence of Hadean continental crust. One argument is based on low crystallization temperatures of Hadean zircons that have been determined using a novel geothermometer based on the Ti content of zircons in equilibrium with rutile. The second argument is based on using the trace element abundances in zircons to calculate their parental melt compositions, especially the rare earth elements. Here we demonstrate that zircons that grow from a melt formed by basalt differentiation at modern mid-ocean ridges cannot be unambiguously distinguished from Hadean zircons on either of these grounds. Thus, we conclude that the trace element compositions of Hadean zircons are permissive of models that do not include the generation of continental crust in the Hadean.