In order to characterize the spin-spin exchange interactions responsible for the Type-E' antiferromagnetic order in inhomogeneous RNiO3 perovskites (R=Y or rare earth), the pressure dependence of the Néel temperature T(N) was systematically measured for samples with T(N)<T(IM) and T(N)=T(IM); T(IM) is an insulator-metal transition temperature. Analysis of the results shows that, as for superexchange, perturbation theory can be used to describe the interatomic exchange interactions for T(N)<T(IM), but the perturbation theory breaks down where T(N) approaches T(IM).