Jean:
To me, there are two schools of painting and color - the complementary analogous (CA) way, and the chromatic value (CV) way.
The CA system deals ok with hue and less well with chroma and not at all with value. The hues are based on the three primary system and chroma is dealt with by neutralizing with opposites. the problem with this is that invariably, you contaminate your hue.
The CV system starts with more accurate hues, and addresses them within a value scale. To ensure that hues are not contaminated, you neutralize with an equal value gray.
The Wilcox system seems to be a differing way of looking at the CA system, but still does nothing to address value and his chroma system depends on mixing specific brands (namely his) of paint to achieve clean neutralizations. What about hue variations within brands of Hansa Yellow? What if they stop making Hansa Yellow? This guy trying to sell you something as part of his system - what happens when he goes out of business? Further, what quality level are his paints? It seems that he has taken the tertiaries out of the Munsell color scale and dumped the primaries.
I am not saying that his system cannot work, just that I would be cautious about systems that are dependent on specific products, colors, etc. And be wary if someone is trying to "sell you a system" with "products" and especially paints.
Color theory and use should be free. Yes, you do need paint, but you should choose the type and brand yourself and know the quality of the product from its reputation on the market - again, my opinion.
I hope that helps!