Current predictions for the ratio of phi -> K^+K^-/K_LK_S decay rates exceed the corresponding experimental value in about five standard deviations. By far, the dominant sources of isospin breaking to this ratio are the phase-space (52%) and the electromagnetic radiative (4.3%, computed within scalar QED) corrections. Here we estimate the effects of the electromagnetic structure of kaons and other model-dependent contributions into the radiative corrections.