Because I really do want to get away from this, and don't really want to leave a question in the air, I'll give my version of the simple answer. Tom, I'm simply asking posing questions so you can order your thoughts.
So here goes. There is a centre of perspective where apparent relationships between objects are preserved and we see a natural perspective, or one closest to that we would see if standing at the spot the camera took the photo.
If we take a photo of a distant barn (and I'm deliberately using an object in the landscape that has a linear perspective to preserve), it is foreshortened as geometry dictates.
If we view that barn in the photo at a point in front of the centre of perspective then the depth of that barn appears compressed, at the point it looks normal beyond that point it looks longer, up to a point because as we move further away to view the image the barn in the image reduces in scale and so looks as though it's further away to a point where we stop seeing the perspective altogether.
The barn in the photo always looks like a distant barn we simply make errors of assumption about it's depth when we view at a point other than the center of perspective. There is no point where at which you can view a distant object in a photo where it will take on the appearance of a wide angle view or wide angle distortion.
Similarly there is no point as you move closer to a wide angle shot of a near object where it will take on the perspective of a distant object. We simply make errors of assumption about it's depth. And there's also a limit about how close you can get to the photo.
So the following statement is incorrect:
The perceptual side comes when we define natural, foreshortened and elongated against viewing distance. Though it's tough to show this as human perception generally looks at an image, makes assumptions about perspective, preserves consistency of understanding and so in effect perspective in images appears quite static over a wide range of viewing distances.
The image is always an image of a foreshortened barn, it never changes. So when we view an image of a distant and therefore foreshortened barn and see it as normal rather than foreshortened it means that you do not see the absolute perspective in an image at the centre of perspective, you see a correct one.
This perceptual effect takes a little more explaining, of why you see the barn at the correct size rather than the absolute perspective of the foreshortened barn as contained in the image.
But everything below the quote can effectively be ignored if all you require is a working understanding.