In recent years it has become clear that complex oxides provide an exceptional platform for the discovery of new physics as well as a considerable challenge to our understanding of correlated electrons. The tendency of these materials to display nanoscale electronic and magnetic inhomogeneity is a good example. Here, we have applied a variety of experimental techniques to investigate this magneto-electronic phase separation in a model system - the doped cobaltite La1-xSrxCoO3. Comparing experimental data over a wide range of doping with statistical simulations, we conclude that the magneto-electronic inhomogeneity is driven solely by inevitable local compositional fluctuations at nanoscopic length scales. The phase separation is thus doping fluctuation-driven rather than electronically driven, meaning that more complex electronic phase separation models are not required to understand the observed phenomena in this material.