Wrong.
My probe signal is a 19khz sine wave.
My noise signal is a 1.5kHz sine wave.
If you play the 19kHz sine wave back at 90dB SPL (assuming your system can do that), at what level can you hear the 1.5kHz sine wave?
You think it's inaudible at 30dB SPL?
Really? No.
You can do the same thing, give or take, with a 40Hz sine wave and a 3kHz sine wave as the 'error' signal.
Once you stick strictly to SNR (ThD, whatever) and don't specify the actual error spectrum, you've really widened the requirements, and yes, then you need to simply stay below absolute threshold of hearing, give or take.