See the following video from the awesome Mike Browne to see how FoV affects perspective & compression.
https://www.youtube.com/watch?v=t3A3SnPFPk0
Good illustration of perspective/compression, but they are moving the camera when they move to the longer lens.
At 3:12: "Now because of the magnification aspect Jayne's had to move back with the camera in order for it to fit."
When he moves to the longer focal length lens, he moves the camera back. It is this change in position that results in a change in perspective. The longer focal length results in a narrower field of view. If they had kept the camera in the same position, you would only see a portion of the rock in the foreground, and the compression would have remained unchanged.
Similarly, at 4:09, when discussing perspective and moving to the longer lens, he says "it's the same shot, keeping this stone the same size in the picture."
So once again, they have moved the camera, and the change in perspective results from moving the camera back. Zooming the lens (or using a longer focal length lens) allows him to reframe the subject (the rock), but it is the change in position that results in a change in perspective.
He does make the statement that long lenses flatten things together (sometimes described as long lenses compressing the scene), but they only have that effect when you change your position (relative to a normal or wide lens) by moving back and reframing your shot. So for practical purposes, you will frequently observe more compression with a longer lens, but that is because you need to stand further away to use it to reframe your subject.
Think of it this way, the camera can only see the world from where it is sitting. No matter what lens you put in front of it, the relationship of objects in the foreground and background does not change. You have to move the camera.
Like I said, a can of worms.
EDIT: Returning to the question that I originally replied to, this is why a given lens (in this case, an 85mm) will have more compression if used on a crop-sensor camera than on a full-frame camera. The answer is (still) no and yes. If you do not move the camera, putting the lens on a crop-sensor body merely crops the field of view. It does not affect compression. However, if you move back in order to achieve the "same" framing of your subject, you will change the perspective, and you will then see more compression than when you had it mounted on a full-frame body and were standing closer. So when used to achieve similar framing as on a full-frame body, a given lens will exhibit more background compression when used on a crop-sensor body (because you have to move to reframe the shot).