To understand which populations and species are most sensitive to climate change, studies correlate time series of climate variables with those of traits important for population dynamics, and subsequently compare which aspects of a species' ecology or life-history best explain variation in climate sensitivity. Often large-scale oceanic climate indices (LOCIs) are used as a proxy for local climatic drivers, with many studies reporting geographic gradients in climate sensitivity to LOCIs (e.g. suggesting that species living further from the equator are relatively climate sensitive). However, the relationship between LOCIs and local weather variables also varies geographically, raising the possibility that apparent intra- and inter-specific differences in climate sensitivity to LOCIs could also reflect geographic variation in how well LOCIs function as a proxy for local climatic drivers. This hypothesis is rarely tested due to lack of knowledge about the specific local climatic drivers. Here we show, using reproductive and climate data from 16 long-term population studies of 7 Australian fairy-wren species (Malurus genus), that the use of LOCIs can result in 1) strong overestimation of the amount of inter-specific variation in climate sensitivity and 2) spurious patterns, particularly geographic gradients. Consequently a paradox emerges: LOCIs often explain much of the temporal variation in traits important for population dynamics, but the common usage of LOCIs may prevent meaningful intra- and inter-specific comparisons of climate sensitivities over large spatial scales. Our results thus may offer an alternative interpretation of the widely reported geographic gradients in sensitivity to LOCIs. Future progress will likely require better knowledge about the identity and temporal features of local environmental drivers of population dynamics.