Here is an article from Sony which pretty much has it right in terms of correctly differentiating exposure* and image lightness.
www.sony.com/electronics/support/articles/00267925
The article starts off with:
"Exposure is the amount of light coming into the camera when shooting a photograph."
which is very similar to - amount of light that struck the sensor per unit area while the shutter was open.
It then says:
"The amount of light is determined by the aperture and shutter speed."
which should really also include scene luminance. The important thing to note is that Sony say that ISO is not part of the exposure as they define exposure.
They then go on to say:
"These, combined with ISO sensitivity, determine the brightness of a photograph."
which is effectively what I and many others have been saying in that ISO is an image lightness, not exposure*, parameter.
Therefore this article from Sony also confirms what I posted earlier:
For a given scene lighting:
f/8, 1/400s, ISO 200
and
f/8, 1/200s, ISO 100
will output the same image lightness (or brightness if you like) but the ISO 200 shot will have had only 1/2 the exposure* of the ISO 100 shot and so the ISO 200 shot will have more visible noise than the ISO 100 shot.
The bottom line here is that Sony are saying that according to their definition of exposure, exposure is not how light or dark an image looks.
* exposure - amount of light that struck the sensor per unit area while the shutter was open
** optimal exposure - the maximum exposure* within dof and motion blur requirements without clipping important highlights.
*** under exposed - more exposure* could have been added with the DOF and blur constraints still being met without clipping important highlights.