It's a good point, I wasn't precise in my language. A good way to understand it is that if two different colors have the same lightness (or hue, or saturation) in some color space, that "predicts" that they will be perceived to have the same lightness as well. It's impossible to get these predictions exactly right (in part because actual perception depends on so many variables), but some can be better than others.

Another useful function of a color space is to predict the threshold of when two similar colors are just barely perceptibly different.