Number of LEDs?

Am I misunderstanding how RGB LEDs work? I thought that if you were to illuminate the red portion as well as the blue portion it would "create" a new color, in this case purple. If you were to mix the various colors and brightnesses, you would produce many different colors. Am I wrong?

How else would the table produce that rainbowing effect? Here is the link again since it is on the first page: 64 RGB-LED color wave table (Arduino, 12x TLC5940) - YouTube