It's not completely accurate to say that looking at just three faces is enough to solve the cube. A permutation of three edges serves as a simple counterexample. In fact, all six sides have to be scanned, although (if I'm not wrong) five is enough most of the time.

Unless you're referring to the last layer part, where one look is enough, but the standard computer algorithms (Kociemba's for example) don't use a layer-by-layer approach at all.