An unusual effect was discovered in Li et al (2010 J. Solid State Chem. 183 1388): the substitution of nonmagnetic low-spin Co(3+) in LaCoO3 by the formally isoelectronic and also nonmagnetic Rh(3+) led, surprisingly, to a rapid appearance of magnetism in LaCo(1-x)Rh(x)O3, even for small amounts of doping. Different explanations for this effect were proposed in the literature. To clarify the situation we carried out unbiased ab initio calculations of this system. We concluded that, in agreement with the original assumption of Li et al, but in contrast with later statements (Knizek et al 2012 Phys. Rev. B 85 134401), this effect is caused by the valence change ('redox reaction') Co(3+) + Rh(3+) → Co(2+) + Rh(4+), which creates magnetic Co(2+) and Rh(4+) ions. For the half-filled case LaCo1/2Rh1/2O3 we obtained the state with charge ordering of Co(2+) and Rh(4+) ions, which according to our calculations are antiferromagnetically coupled. The obtained results reasonably explain the observed behavior of the magnetic susceptibility of LaCo(1-x)Rh(x)O3, and the novel state predicted at half-doping could be verified experimentally by detailed structural and magnetic studies and by x-ray absorption spectroscopy.