One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been shown that heterogeneity can lower the epidemic threshold at which epidemics can invade the system. Network heterogeneity can thus allow diseases with lower transmission probabilities to persist and spread. Here, we point out that for real world applications, this result should not be regarded independently of the intra-individual heterogeneity between people. Our results show that, if heterogeneity among people is taken into account, networks that are more heterogeneous in connectivity can be more resistant to epidemic spreading. We study a susceptible-infected-susceptible model with adaptive disease avoidance. Results from this model suggest that this reversal of the effect of network heterogeneity is likely to occur in populations in which the individuals are aware of their subjective disease risk. For epidemiology, this implies that network heterogeneity should not be studied in isolation.