Meanwhile, a 15 khz tone on a CD has three samples per crest. With three samples there is no way to diffrentiate between a sine wave, a square wave, or a sawtooth wave; all will sound exactly the same.
True, but they would sound the same on an analog turntable as well.
What separates a sawtooth wave and a square wave from a sine wave, is their harmonics. While a sine wave have no harmonics, a sawtooth wave and a square wave can be decomposed into a superposition of sine waves whos frequencies are integer multiples of their fundamental frequencies. Hence, the second harmonics of the square and sawtooth waves are at 30kHz, way above the limit for what we can hear.