Actually, the author is wrong. It has nothing to with how far something is from the background. It has nothing to do with camera position or focal length. It has nothing to do with linear perspective at all.
The effect of compression, or expansion, the roundness and depth you see with "wide-angle" images, is the result of viewing angle. If your viewing angle, the angular size of the image from where you are standing (or sitting), is the same as the angular field of view of the camera, then the image will look normal with no compression effects. If your viewing angle is great than the taking (camera) angle, then you will perceive compression. If your viewing angle is less than the taking angle, then you perceive more depth. This is also known as apparent perspective.
And this is the only reason we perceive this effect in photography. It is the only way we can see the world at a distance different from where we are (or would be). This is easy to prove. When you are at a party, the person standing across the room does not look any more compressed than the person standing next to you. If you look at a tree trunk with binoculars, the trunk looks flat, like a cut out, but, if you view without binoculars, the roundness of the trunk looks natural. It is simply an angular difference in the views. And it also works for prints. If you are in a gallery, standing next to a large print, the image will look compressed. Walk on the other side of the room and view the same print, and the print will appear to have more depth.
Compression is a perceptual effect of the viewer.