Dear God, Ray!
Now, at last, I understand the fascination with oriental transvestites: you will never have to face (groan) that situation ever, never, again!
But from the photographic perspective - oh dear - the thing has nothing to do with wide-angle lenses nor any other kind of glass: perspective is totally due to the viewer's/camera's location vis a vis the subject. Exactly as you pointed out with your comparison between two cameras. In essence, you could only think of wides and perspective as distortions of the one caused by the other if you either did not know that lenses have nothig to do with it or were simply trying to stoke fires within the tinder-dry forest of LuLa.
Devil's advocate, you!
First let me dispel any notion that I might have any sexual proclivities for transvestites. I have photographed them in Thailand because they wish to be photographed and because they are easy to photograph because they are so proud of their transformation from male into female and are not shy to show off the results. In a sense, transvestites, or perhaps more correctly, transexuals, are walking works of art; a product of the surgeon's knife and hormonal treatment. I make no moral judgement here. The idea might be repulsive to some. However, when I show my transexual shots to others, they often cannot believe that they are actually looking at a bloke, when I tell them. It's almost like, "I can't believe it's not butter" .
To get back to perspective, it seems to me there is a lot of confusion about the naked eye's true focal length and field of view. I get the impression from a Google search that it's about 22-24mm with an FoV of 140-160 degrees. Some reports place it at 180 degrees, but the problem here is peripheral vision. If one includes peripheral vision in the field of view, human vision may be as wide as an ultra-wide-angle lens.
However, peripheral vision is only good for detecting movement and very rough degrees of light and shade. The angle of view of human vision that takes in full detail, or sufficient detail to make accurate perspective assessments, is actually quite narrow. At least mine is. Perhaps I'm abnormal.
There's also the psychological aspect of the brain being familiar with certain results, through habit. We are not objective creatures (or robots), automatically adjusting our perceptions precisely according to distance to subject.
Devil's Advocate or not, I still think that wide-angle lenses create an appearance
of distorted perspective because they provide perspective detail in that peripheral area of human vision that normally lacks such detail.
If we turn to the telephoto effect, a similar principle applies, but to opposite effect. The naked eye takes in a wider
FoV, in full detail and excluding peripheral vision, that the camera shot does not provide. We therefore get the impression from the photographic image that the distance between foreground and background has been compressed.