As the statement it written, it is wrong. A simple geometric argument shows that the perspective only depends on the distance from the camera to the subject, regardless of the field of view, regardless of the lens.
But why believe a geometric argument? We can look for ourselves at a real life example. This image was taken with the Lumix G 100-300mm lens at 300mm:
In the image, it looks like the construction cranes are just behind the neon "Freia" logo on the front rooftop. But in reality, the distance is 1 km. This is what we normally call a compressed perspective.
But is it the long focal length which produces the compressed perspective, as the statement initiating this article? We can see for ourselves, by setting the lens to 100mm, and photographing from the same point. That gives this image:
Does this image have a different perspective? We can crop the centre of the 100mm image and compare it with the 300mm image:
We see that the images are exactly identical. There is no difference in the perspective, demonstrating that the perspective only depends on the placement of the camera, not the focal length.
On the other hand, if I change the point from which I am photographing, as well as change the focal length, then I get a totally different perspective, as illustrated:
Here is the same building photographed much closer with the Lumix G 14mm f/2.5, a wide angle lens:
Now, the perspective is not compressed anymore. But was this due to the wide angle lens? No, I would say, it is because I went closer to the subject.
But, it was the wide angle lens which allowed me to go closer to the subject. Just as it was the tele lens which allowed me to go far away from the subject, to create a compressed perspective.
So while it is not true to say that a tele lens compresses the perspective, it is true that the tele lens allows you to step further from the subject, to achieve a compressed perspective. So, at the end of the day, it is perhaps not so wrong to say that the tele lens compresses the perspective, as this is what you achieve when using the lens anyway.
Having some focal length range available, either as a superzoom lens, or as some different prime lenses, is useful. It allows you to achieve various perspectives, by varying the distance to the subject.