If both are right then can someone explain in straightforward, relatively simple terms how these can be reconciled and if the paint colour primaries are wrong then what is the flaw and why is it that red, yellow and blue are wrong?
I've been trying to think of a relatively simple way of explaining this. Perhaps one way is to say there is really one set of primary colours as far as our eyes are concerned, and that the second set emerges as a way of "filtering" them.
I don't think that there IS a simple, straightforward way of explaining this. Well, at least in not less than an hour or so, with open-minded people. You have to be able to temporarily set aside what you "know" about this from color photography.
I see two ways of "knowing" about color (beyond what we directly see). The first uses what is known as "colorimetery," and one of the best "simple" explanations, to my way of thinking, was in the 1963
Feynman Lectures on Physics. Specifically chapter 35, "Color Vision." A brief excerpt,
Now a question is, what are the correct primary colors to use? There is no such thing as “the” correct primary colors for the mixing of lights. There may be, for practical purposes, three paints that are more useful than others for getting a greater variety of mixed pigments, but we are not discussing that matter now. Any three differently colored lights whatsoever can always be mixed in the correct proportion to produce any color whatsoever.
Be aware that Feynman is not saying exactly what it seems like. With 3 physical lights, there are always some colors that cannot actually be matched; it would be necessary to use negative values of some light(s). However, shining some of this light on the reference sample is mathematically equivalent to a "negative light" on the other side, so this demonstrates the mathematical "match."
He expounds on this...
We may ask whether there are three colors that come only with positive amounts for all mixings. The answer is no. Every set of three primaries requires negative amounts for some colors, and therefore there is no unique way to define a primary. In elementary books they are said to be red, green, and blue, but that is merely because with these a wider range of colors is available without minus signs for some of the combinations.
My second way of "knowing" is based on the spectral nature of light reaching the eye. A group called the CIE has a thing called the "Standard Observer," where something called "color-matching functions" have been experimentally determined. If one knows the spectral makeup of the light reaching the eye (multiply the spectral makeup of the light source times the spectral transmission of the filter), then it is possible to specify where this light would fall, in some color space, with respect to an adapted "white point."
The best "simple" explanation (to me) that I know of is in a booklet (1998? about 100 pages) called the "Color_Primer" by Fred Bunting, that I believe can be found on Xrite's website. I think most photographer's will find their eyes glazing over by about page 10, but if you can make it through, you will have a much deeper understanding of things.
I personally grew up with the system of color photography, with red, green, and blue (additive) primaries, and cyan, magenta, and yellow (subtractive) secondaries, and I had a very hard time getting over that. My breakthrough was when I first realized that there is no rigid physical definition of those colors, so they can sort of be whatever one wants them to be. The more important thing is that one designs the spectral sensitivities of the color paper, for example, to be matched with the dyes in the film, which are ideally the same as the printing filters.
ps: I don't know if I have the patience to argue these issues, which is why I give the references. But I'll hang in for a while if anyone cares to discuss. Thanks for reading, assuming you got to here!