I have an inkling of what this must look like.
To do this one must have basic knowledge of wave-form math and music theory.

Our hearing can perceive several octaves of music. High 'e' and low 'e' have two fundamental similarities. They both sound similar, and the one is exactly double the wave form of the other. High 'e' is said to be 'brighter' than low 'e'.

In visible light we can only see 1 range of colors. In musical terms this is analogous to being able to hear only 1 octave.

So if we could see light with twice the frequency of middle-green, it would actually look much like green except it would be 'brighter' and have a perceptible 'higher' energy value. Low green would be 'dull' in much the same way that low 'e' is a dull version of middle 'e'.

Now, how can we be sure that ALL people can actually only see the visible spectrum? Well we cannot be certain, we can only guess that MOST people do. We cannot test everyone, all the time.

Any person that claims to be able to see things that others cannot, is said to be suffering from 'hallucinations'. Is it not highly probable that some people under certain conditions can actually see things that others cannot?

Now if these people are a significantly small minority, would it also not follow that they would be seen perhaps as 'mutants', or 'insane'?

And, given that such is occurring, it would be presumptuous to believe that all such people were actually seeing the same phenomena. Some may be seeing higher light, other's lower light.

Also, perhaps it is possible to 'see' bands of electromagnetic waves that are actually far removed from the spectrum of visible light, and be blind to the light in between. The faculty of perception may not be static, it may even be moving and available only under rare conditions. Musicians have off days in the same manner.

Sense perception requires training too. As musicians sharpen their skills, they are able to distinguish sound in far more detail than the layman's ear. They can pick out tiny errors in music which us normal folk are blind to. So to actually prove this idea is not something that can be done with a simple one-off test.

As an amateur muso, I know that when I do not play for a week or more, my ability lapses very quickly. So concentrated training of such notions requires nurturing, patience, and prejudgemental pre-concieved notions can be a great hindrance.

Are there any examples of people claiming to be able to see things that others cannot?

;-j