Put the camera on a tripod near you, say 2-3 ft, and take a shot at 30mm and a shot at 50, 60 whatever. Crop them both for a portrait from ear to ear (same FOV, same distance, different focal lengths...) Do you see any perspective distortion in the wide angle? Once you are far enough, you don't see the perspective distortion (as in the photos you linked).
It is not 'perspective distortion' that you see in a very wide angle lens, but barrel or pincushion optical distortion associated with representing a spherical optical space in a rectilinear manner. Two very different types of distortion!
- The Canon 28mm shows -1.2% barrel distortion on FF and on APS-C as well!
- The even wider 24mm shows -1.4% barrel on FF, but drops to -0.74% barrel distortion on APS-C.
- The yet wider 17mm TSE shows -1.1% barrel on FF (less than both more moderate wide angle lenses!) and was not tested on APS-C.
I can assure you that the 17mm would exhibit the most PERSPECTIVE distortion used very close to the subject, in spite of the fact that it has the least BARREL distortion! And at 10' all three would have no PERSPECTIVE distortion (10' does not induce perspective distortion. if the focal plane is perfectly parallel to the ground and parallel to the subject) while nevertheless exhibiting the above amounts of BARREL distortion