It's true for a triangle wave and a square wave, depending on if the output has a reconstruction filter doing linear interpolations between samples. You cannot accurately sample a 22.05 kHz sine wave (or any other "complex" waveform) with a 44.1 kHz sample rate.
You're incorrect. A 44.1kHz sample rate can recreate a 22.05kHz sine wave. Your mental model for a digital signal isn't correct. It's not making stair steps nor is it making triangular waves.
