We use publicly available galaxy merger trees, obtained applying semi-analytic techniques to a large high-resolution cosmological simulation, to study the environmental history of group and cluster galaxies. Our results highlight the existence of an intrinsic history bias which makes the nature versus nurture (as well as the mass versus environment) debate inherently ill posed. In particular, we show that (i) surviving massive satellites were accreted later than their less massive counterparts, from more massive haloes and (ii) the mixing of galaxy populations is incomplete during halo assembly, which creates a correlation between the time a galaxy becomes satellite and its present distance from the parent halo centre. The weakest trends are found for the most massive satellites, as a result of efficient dynamical friction and late formation times of massive haloes. A large fraction of the most massive group/cluster members are accreted on to the main progenitor of the final halo as central galaxies, while about half of the galaxies with low and intermediate stellar masses are accreted as satellites. Large fractions of group and cluster galaxies (in particular those of low stellar mass) have therefore been ‘pre-processed’ as satellites of groups with mass ∼1013 M⊙. To quantify the relevance of hierarchical structure growth on the observed environmental trends, we have considered observational estimates of the passive galaxy fractions and their variation as a function of halo mass and clustercentric distance. Comparisons with our theoretical predictions require relatively long times (∼5–7 Gyr) for the suppression of star formation in group and cluster satellites. It is unclear how such a gentle mode of strangulation can be achieved by simply relaxing the assumption of instantaneous stripping of the hot gas reservoir associated with accreting galaxies, or if the difficulties encountered by recent galaxy formation models in reproducing the observed trends signal a more fundamental problem with the treatment of star formation and feedback in these galaxies.