In the social sciences, within the explanatory paradigm of structural individualism, a theory of action—like rational choice theory—models how individuals behave and interact at the micro level in order to explain macro-observations as the aggregation of these individuals’ actions. A central epistemological issue is that such theoretical models are stuck in a dilemma between falsity of their basic assumptions and triviality of their explanation. On the one hand, models which have had great empirical success often rest on unrealistic or even knowingly false assumptions; on the other hand, more complex models, with additional more realistic hypotheses, can (trivially) adapt to a wide range of situations and thus lose their explanatory power. My purpose here is epistemological and consists in wondering to what extent demanding realistic assumptions in such cases is a relevant criterion with respect to the acceptance of a given explanatory model. Via analogical reasoning with physics, I argue that this criterion seems too strong, and it is also irrelevant. General physical principles are not just idealised or unrealistic. They can also be formulated in many different yet equivalent ways that do not imply the same fundamental unobservable entities or phenomena. However, the classification of phenomena that such principles allow us to highlight does not depend, at the end, on any particular formulation of these basic assumptions. This suggests that some hypotheses in theoretical models are not genuine empirical statements that could be independently tested but only substrates of modelling embodying a classification principle. Thus, I develop a structural invariance criterion that I then apply to rational choice models in the social sciences. I argue that this criterion allows us to escape from the epistemological dilemma without condemning formal approaches like rational choice theory for their lack of realisticness or for being stuck to a merely anti-realist viewpoint.