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All I'm worried about is the difference in magnification of closer and far objects. The 'long nose' effect. Perspective distortion. This is what I am talking about when I'm talking distortion. I took some pics today and to be honest... the noses looked a little long.
The only lenses that introduce severe distortions are fish eye lenses, which introduce a completely different pincussion distortion.
Perspective distortion that is attributed to wide angle lenses is purely a factor of being too close to the subject. - It's down to changes in the relative distances to different parts of the subject.
Looking at some extreme cases to illustrate - If your only an inch from someones nose, then the rest of their cheaks will be around three times as far away as the tip of the nose. With a super telephoto the nearest point on the subject might be 50' away, the extra 1-2" to the rest of their face is hardly noticable.
Try some experiments with any zoom (or pair of primes of different focal lengths). Take a photo with the longer focal length of a suitable subject, then another FROM THE SAME POINT using the widest setting. Crop the wide image to match the FOV of the zoomed in shot, and compare perspective - no change.
Using a SINGLE FOCAL LENGTH take two images of the same subject, one form as close as practical, the second from at least 4 times as far away. Crop the wide shot & compare - the closer shot will have more perspective. The effect is typically more noticable with wide angle lenses as it's more practical to get closer with them, but with extension tubes it can be shown easily enough with telephoto lenses too.