Yes. An amp with a -3 dB of 300 kHz will not "more accurately" reproduce 20 kHz than an amp with a -3 dB of 200 kHz. There is a huge and fundamental misunderstanding going on here.
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Not so, says this article from the influential Roger Russell site:
http://www.roger-russell.com/truth/campbellsineward.htm
Of course the article was written in 1961, and we've learned quite a bit since about hearing since then.
One of the author's theories is that we hear tie direction that sounds come from by means of detecting phase shift of signals between the ears.
If our ears can detect phase shift or timing differences then they can detect the phase or timing difference between signals that vary only in terms of their phase shift or timing of the components they are made up of.
At this time we know that this is both true and false. Our ears do detect phase shift and timing difference below about 1000 Hz, but not so much above. Above about 1000 Hz our ears can detect the direction that sounds come from, but this is done by means of the changes in the frequency response of those signals by the shape of our head. These are called HRTFs.