Extension Tubes and the Inverse Square Law

Hello Forum.

I have been in a discussion with a friend about close up imaging with tubes and bellows. A question has arisen from that, and with which I need some help.

It is my understanding that when extending a lens with tubes or bellows, that its light at the film plane falls off with extension in lock step with the inverse square law.

For example, suppose we have a 50mm lens set to its infinity setting. Its focal length is 50mm. Now suppose that we extend that with a bellows or tubes to include another 50mm, now totaling 100mm. Suppose also that the aperture of the lens stayed at what is marked as f4 on the lens barrel.

It is my understanding that while the physical diameter of the aperture remains constant, the effective aperture changes from f4 to f8, two stops. And the light available at the film plane (because of diverging transmitted light rays coming from the open aperture area of the lens) is one fourth as much. This, I understand, agrees with the inverse square law.

I have been told that in close up imaging, explaining the light at the film plane in terms of the inverse square law is wrong to do, and oversimplified. I'm puzzled as to what is wrong about the way I am thinking about it.

Doesn't the inverse square law apply between lens and film plane just as it applies outside the camera? What am I missing in this?

Thanks for your insight in this.