I noticed a recent thread which gravitated towards this topic was closed because of rising tempers and inferred insults. This is my attempt to try to explain what's going on and why both sides of the argument could be considered correct, but each from its own perspective (pun intended).
There's no doubt that a wide-angle lens can create an appearance of an unnaturally enlarged foreground, compared with the size of the objects in the background. Likewise, a telephoto lens can create the opposite effect of appearing to exaggerate the closeness of objects in the background, such as a mountain immediately behind the subject that looks so close but is actually quite far away.
From a subjective point of view, perspective is all about the eye/brain attempting to work out the distances of objects in the picture by assessing their relative size to each other. In order to do this, one has to be able to recognise what the object in the picture actually is. A picture of unrecognisable objects becomes effectively an abstract and as a consequence perspective tends to become less of an issue, although it's alway apparent that any object which appears to be partially obscured by another object must obviously be behind and further away than the object which does the obscuring.
The following shot was a sort of joke snapshot of a fellow traveller in Nepal who seemed rather fascinated with the unusual shape and bulk of my Sigma 15-30mm zoom with protruding, bulbous front element. I explained it was an ultra-wide-angle lens, and took the following portrait with the front of the lens about a foot from his face, which he found rather amusing as you can see.
I used a 5D. But supposing I had used a P&S camera with 15mm lens from the same distance. That would not have been wide angle, but medium telephoto. All I would have captured would have been the guy's nose. I would not be able to assess whether or not the guy's nose appears unnaturally large in relation to the rest of his face, and the background, because the rest of the face would not have been in the picture. Large and small are relative terms.
If I had had the patience to do a 20 image stitch with the P&S camera with 15mm lens, of this subject, (assuming the subject were able to remain perfectly still which of course would not have been possible), then the resulting stitch would have looked identical in terms of perspective as the single shot with the 5D and 15mm lens, ignoring lens defects such as distortion. It would differ, of course, in terms of DR, tonality, noise and resolution etc, but not in terms of perspective.
The question now arises, can both images, the single shot with the 5D and the stitched shot with the P&S, both using the same focal length of lens from the same distance, be considered as a distortion of perspective?
I would maintain that they can, from the subjective point of view, but not from the objective science of the principles of optics. In these examples of wide-angle or telephoto lens usage, the camera delivers results which the eye can never see, unaided. The perspective therefore appears distorted because in real life we simply don't get such a wide (or narrow) angle of view using our eyes. We're seeing something never seen before, until wide-angle lenses (and telephoto lenses) were developed.
Imagine you are making love to a beautiful lady with a perfectly shaped nose. You're lying on top of her with your face just 6 inches from hers. There's no sense at all that her nose has enlarged in relation to the rest of her face, because the closer you get the narrower your angle of view.
Suddenly, your eyesight is bestowed with the wide-angle capability of a 12mm lens on a 5D. You see everything in the room in clear detail. Your lover's nose appears huge. It's the same size as it was before, but now in relation to everything else you see, it appears relatively huge. Offputting, maybe?