How could visible light be in pitch-black? Can it be?
Black is not a color; it is the absence of light.
I think you interpret the sentence as "the light is black", but it's just a way of saying "there is no light (at optical wavelengths, but there is at radio wavelengths)".
In my opinion this is not a good way of explaining the CMB. The sky is not black at any wavelengths, but has a background radiation at all wavelengths. In the optical, this background originates (primarily) from the integrated light from stars; in the microwave it originates (primarily) from the afterglow of Big Bang; in the infrared from dust, etc.
See the figure in this answer to a question about the number density of CMB photons, to see how large the background is in various wavelength regions.