The point is you can fool the eye into seeing white light when the spectrum isn't remotely approximating "white". All you have to go on is the responses of the three different types of colour receptor in your eye. Balance those responses in the right way and it doesn't matter what the spectrum is like, you see white. Think about what you are seeing when you see "white" on a computer screen -- it is the sum of light output by red, green and blue pixels. This spectrum is very different from sunlight, yet both are seen as white.
This kind of thing is fortunate for art or matching up colours would be a nightmare.