We present fully differential cross sections (FDCS) for single ionization of helium by heavy-ion impact for a wide range of kinematical conditions. The effect of the frozen core approximation is studied by comparing 3-body and 4-body models, and examining in detail the differences between the two models. In general, four major theoretical differences between the models are identified, and the effect of each difference is individually studied. Results of this study reveal that the primary source of the discrepancies between the 3-body and 4-body FDCS is the perturbation resulting from the initial state interaction of the projectile with the target atom and the final state distorting potential for the ionized electron. This is in agreement with results previously obtained for electron-impact ionization of helium.