Ok so rendering: You just take black paint and add it to the local color or the shadow side and take white paint and add it to the local color of the light side right?

NO

Light and color are a bit more complex: You need to consider the actual color/temperature of the light (for example indoor lights tend to be yellow, outdoor light tends to be blue). 

In addition you need to consider the fact that every object that is lit becomes a weaker light source in that objects local color. Therefore every objects that is surrounded by other objects (almost every single lighting scenario) is influenced by multiple light sources and multiple hues. 

We can see the bounce back of colored light most clearly in smooth (mirror like) surfaces like the examples below....

Also notice the influence of the orange reflecting orange light into the lemon and the lemon reflecting yellow light onto the orange....

Here's another example of a digital painter thinking about the color influence of citrus fruit....

Color Influence in perception and design

Remember that color, shape, value, is relative to what it's surrounded by. In addition our brain will shift our visual perception of value to level adjust our vision/perception.

To prove the theory stare at the yellow box or the red triangle intensely for 30-60 seconds then stare at the blank white space after it. You will notice that the after image is the exact complimentary color of the shape you had been staring at.

The center green block here appears to shift value but it's actually a solid colored block.

Here the character appears to have warmer skin and cooler hair, but the image is really monochromatic in HUE. The hair is the same HUE as the skin but because it's desaturated it appears cooler the skin which is more more saturated.

Three more examples of how relativity affects value and scale. The first example of relative value is a particularly powerful example.

michaelanthonygalante.blogspot.com

Ebbinghaus Illusion www.dailycognition.com