^^ Its not the ability to hear to 20KHz or beyond that is why you can hear differences in bandwidth outside of the 'audio region'. Please read Kijanki's post above.
When you have a rolloff at or near the audio passband, its audible as phase shift down to 1/3rd to 1/10th the cutoff frequency, depending to a certain extent to the steepness of the rolloff. Phase shift is converted by the ear/brain system (just as distortion is also) to tonality. The result is a tonal coloration. This is why bandwidth is so important.
When you have a rolloff at or near the audio passband, its audible as phase shift down to 1/3rd to 1/10th the cutoff frequency, depending to a certain extent to the steepness of the rolloff. Phase shift is converted by the ear/brain system (just as distortion is also) to tonality. The result is a tonal coloration. This is why bandwidth is so important.