The spin fluctuation spectra from nonsuperconducting Cu-substituted, and superconducting Co-substituted, BaFe2As2 are compared quantitatively by inelastic neutron scattering measurements and are found to be indistinguishable. Whereas diffraction studies show the appearance of incommensurate spin-density wave order in Co and Ni substituted samples, the magnetic phase diagram for Cu substitution does not display incommensurate order, demonstrating that simple electron counting based on rigid-band concepts is invalid. These results, supported by theoretical calculations, suggest that substitutional impurity effects in the Fe plane play a significant role in controlling magnetism and the appearance of superconductivity, with Cu distinguished by enhanced impurity scattering and split-band behavior.