But what about the indirect illumination (irradiance), like if we used finalgathering for example?
FG on, all settings same as in the last image:
Ugh! What happened? Lamrug.org gave me the answer: http://www.lamrug.org/resources/mayafgtips.html. When a shader gathers irradiance with mi_compute_irradiance, it should normally divide the result by Π, since the irradiance is the energy gathered over the hemisphere above that point. Dividing by Π makes it a color at the point.
So the irradiance is being divided by pi already (this does not apply to maya 5 and earlier). Our irradiance is now actually divided 2 times, because 'Diffuse' is multiplying our irradiance as well - not good. But we can overcome this by a simple trick: we just multiply the irradiance by pi again. By clicking on the 'Irradiance Color' (NOT 'Irradiance'!) the color picker pops up. We then replace the 1.000 in the 'Value' field by pi (3.1415):