As a theoretical construct and property of lenses, unrelated to the making of a picture or composition and therfore excluding the perspective of a potential viewer, the theroetical perspective through the lens is independent of its focal length or the format of the camera it is attached to, and is determined only by the distance between the lens and the theoretical subject.
However, when creating a photographic composition, which most photographers try to do now and again, the focal length of the lens and the format size of the camera will both influence the distance to the subject(s), the size of the subject within the composition and the number of individual subjects or objects within the composition at varying distances from the photographer.
Ok, written a bit complicated, but I translate this basically to:
===In theory, perspective is independent of focal lenght.
But as soon as someone says "a tele optic compresses and a wide optic exaggerates perspective" wich everybody does, the meaning of perspective becomes different and now involves also the field of view of a lens. (As addition to only the position.)
IF we where to insist on using **only** the correct definition of perspective, we could rephrase it as:
To achieve roughly the same framing for a wide and a tele optic, one has to move the tele optic farther away because of its narrower angle of view. As a result the perspective changes. The same view wich occupied a big angle of view from near disctance now occupies a small angle of view and due to this the also perspective differs.
The common speech has shortened this, dont mention the movement because it is implicit (you always have to do it) and instead just takes the focal lenght (wich in play with the sensor size results in a angle of view) as a synonym for the impression that will result, and calls this perspective.
So essentially the abbreviation "a tele optic compresses and a wide optic exaggerates perspective" centers about the practial consequences and dont care about the correct definition. One half is the scientifically correct definition, the other half is the practical consequence. Both can't be neglected. Both are valid in their context, else they wouldnt exist.