Perspective depends on subject distance and NOT focal length. If you stand just as far and have unlimited resolution and crop you get the exact same thing when you crop. I used to have the same misconception.
I think this example leaves out one scenario: Using different focal length when the subject covers the same area in the frame and the resulting change in perspective / relation to the background. Hope this link helps and explains: http://www.luminous-landscape.com/tutorials/dof2.shtml (although it's more for DOF).