That is, “don’t use black for shadows over colored backgrounds.” At every step of my design education I was taught this. For example, when adding a drop shadow as a layer style in Photoshop, don’t just pick a black or a gray but sample a color from the background, then dial it back in opacity until it looks good. This is because shadows in real life are not black. They are darkened versions of whatever they sit on top of, because there is less light. Check out this shadow. If you were trying to recreate that, I don’t think black at any opacity level would get it just right.

Shadows are simply less light reflecting off of a color. Subtle but important thing you learn in art classes.