As somebody who is colour blind and undergone some extensive testing for it, I've been told by several people that the "normal" range of human vision between 400nm to 700nm is more or less an average. Everyone is different, and just as some people can naturally run a mile in 6-7 minutes with little training while others would have trouble walking a mile in 20 minutes, it is the same with our vision. IMO, a more true statement would be that the "weighted average" of human vision is 400 to 700nm, but the extreme ranges *might* go anywhere from say 350, 360nm to perhaps 720 or 730 nm.
For example, even without a yellowed cornea, some people may not see into the UV at all. There are also suggestions - would not go so far as to say a sound theory - that some well known artists from days past had, perhaps without ever knowing it, natural extended vision into either the UV or IR, or perhaps even both. Just as it is claimed that some famous musicians from the past had a naturally extended range of hearing.
Another thing to be aware of is that, at least IMO, the medical profession as a whole really seems to have little interest in this area. Specific example, I am colour blind, but it is very poorly understood. Also, since childhood, I have been extremely sensitive to bright light, but my night vision is superb, and apparently above that of the average person. I cannot tell you how many specialists I have either called or visited over the years, but the response is generally "I don't know" or "well, just live it it". It almost seems to me that if you cannot treat it or fix it right away, and you aren't going to die from it, why bother with it. so I have a small fortune invested in prescription eyeglasses, and I wear them even on cloudy days. You get some weird looks, but you get used to it.
As for "proof", I can understand dealing with skeptical people. In terms of my own night vision, I had trouble even convincing my wife when we were first married. I solved that one real quick one night camping. Walking from our campsite to the washrooms, I left the flashlight behind. I was able to find my way no problem, but my wife keep tripping over rocks or branches in the dark. Even holding her hand she keep tripping or bumping into things. She sure wasn't impressed, but she has never doubted me since. :)