The "compression," or "perspective/foreshortening" is only affected by the camera's distance to the subject, the focal length has nothing to do with it.
Of course a crop sensor may require you to back up a little to achieve the same composition at any given focal length, which will affect the "compression." It is not caused by the sensor or the lens, only by the change in distance to the subject.
There's a similar relationship to DOF, as DOF is smaller when the focus distance is shorter. So if you have to back up to take a photo with a crop sensor, you will also be increasing the dof because of the further distance to the subject. This is why a 50mm f1.4 has a seemingly smaller DOF on a full-frame camera compared to a crop sensor.
One way to think about this issue, is that the "compression" is changing the relationship of objects in a composition, background objects can be obscured in one shot and visible in another if the "compression" is different. Now we all know it's impossible to magically "look around" an blocking object without moving your eye/camera. You must move the position of the camera to perform such a task. There's a trick shot used in movies all the time where they dolly the camera towards or away from the subject while changing the zoom of the lens to compensate for the composition, the result is the compression changing while the main subject stays the same size on screen. The compression change is caused by the moving of the camera, and the composition is compensated for by changing the focal length.