The robustness of biological systems is often depicted as a key system-level emergent property that allows uniform phenotypes in fluctuating environments. Yet, analysis of single-cell signaling responses identified multiple examples of cellular responses with high degrees of heterogeneity. Here we discuss the implications of the observed lack of response accuracy in the context of new observations coming from single-cell approaches. Single-cell approaches provide a new way to measure the abundance of thousands of molecular species in a single-cell. Repeatedly, analysis of cell distributions identifies clusters within these distributions where cells can be grouped into specific cell states. If cells in a population occupy distinct cell states, the observed variable response could in fact be accurate for each cell conditioned on its own internal state. In this view, the observed lack of accuracy, i.e. response heterogeneity, could in fact be beneficial and a potentially regulated feature of cell state variability. Therefore, to truly determine whether the observed response heterogeneity is a desired property or a physical limitation, future analysis of signaling heterogeneity must take into account the internal states of cells in the population.