It's true up to a point. You can hear sounds with an amplitude lower than the total noise level across the audible range. But AIUI you can't hear sounds with a amplitude lower than the noise level in the particular frequency bin (out of the bins into which your ear divides sounds) into which that sound falls. So in the case of 16 bit audio you can resolve a tone down to about -115dB below signal, unlike a measurement device which can resolve it at a much lower level because it can in effect divide the noise floor into an unlimited number of bins .
This is just one tone in the presence of noise with the sound turned up really high - if there was another tone at a much higher level your chances of resolving the -115dB tone are slim, however loud you turned up your stereo..
Alternatively if you take one phon, being the experimentally established quietest sound one can possibly hear*, then that would be 120dB below the loudest sound one could listen to, even for a very short period. Hence we can be pretty sure that something which measures at -120dB could never be heard on anyone's stereo (assuming it was not turned up to a volume which would seriously harm you) ever, even ignoring masking effect or noise floors.
* Yes such a thing exists.