Buckyballs exhibit two seemingly opposing characters. On one hand, they are known to be insoluble in water with all potential chemical properties of being hydrophobic. On the other hand, their pairwise effective interaction in water includes a repulsive solvent-induced contribution. We perform molecular dynamics simulations of the association process of two C60 fullerenes in water at different temperatures in order to reconcile these contradicting observations. For comparison, the simulations were also performed in a nonpolar solvent, and the results were further contrasted with those obtained previously for the association of graphene sheets. Considering the association in water, we find small magnitudes for the enthalpy and entropy changes with small positive slopes as a function of temperature, implying an almost negligible change in the heat capacity at constant pressure. These findings sharply contradict the behavior of typical hydrophobic interactions. The reason for these abnormalities, as well as for the repulsive nature of the solvent-induced interactions, is the shape of the contact state that supports the existence of a distinct type of interfacial waters located between two convex surfaces of two buckyballs. These interfacial waters are characterized by smaller entropy and lower density and form a smaller number of hydrogen bonds with surrounding waters compared with those of the interfacial waters around the dissociated solutes. Thus, upon bringing the C60 fullerenes into contact, the changes associated with the liberation of the latter to bulk waters are opposed by the concomitant conversion of the latter also to the distinct waters between the two spherical solutes. We argue that although the effective pair interaction is not hydrophobic, the solvation properties are hydrophobic. In the hydration free energy of a single solute, there is no contact state. Furthermore, in the solubility at the macroscopic scale, the relative number of these distinct waters around a large aggregate is smaller, and hence, they are not predicted to influence much the solvation properties. Therefore, buckyballs can serve as an example in which hydrophobic interaction cannot be deducted from hydrophobic solvation.