Years of intensive work on perovskite manganites has led to a detailed understanding of the phenomena that emerge from competition between the electronic and lattice degrees of freedom in these correlated electron systems. It is well understood that the related cobaltites provide an additional spin-state degree of freedom. Here, we use the magnetic properties of a particular cobaltite, Pr1-xSrxCoO3 , to demonstrate the vital role played by a further ingredient often negligible in manganites; magnetocrystalline anisotropy. Pr1-xSrxCoO3 exhibits an anomalous ``double magnetic transition'' that cannot be ascribed to a spin-state transition or the usual charge/orbital/antiferromagnetic ordering and has thus far evaded explanation. We show that this is actually due to a coupled structural/magnetocrystalline anisotropy transition driven, in this case, by Pr-O hybridization. The results point to the existence of a distinct class of phenomena in the cobaltites due to the unique interplay between structure and magnetic anisotropy.