I interpreted "compression effect" to mean exactly what you're saying it does. I'm not familiar with what you're saying it does not do. I have never heard of that misconception.
> effect a telephoto has
They're saying that it is not a property of the lens, but rather of the perspective of the scene viewed from a distance. You'd get the same effect using any focal length lens, taking the shot from the same location, and cropping appropriately.
Perhaps in contrast to depth of field which is a property of the lens.
I'm looking at the portraits of the woman on the beach and I'm not understanding how to get from one to the other with cropping. What am I missing?
Of course, on many cameras you then would get a smudgy or pixelated mess.
They could have used the 35mm lens at the same distance as the 150mm lens and simply cropped and the perspective compression would be the same (it'd just be a lower resolution image).