Then I must have supernatural powers of wish-fulfillment, because the difference between the lower & higher bitrate files is real...
As I tried to say above (but evidently wasn't as clear as I should have been), this is NOT a matter of "retrieving information" - that is impossible. HOWEVER, you can run an algorithm designed to make a compressed file sound better to a human ear. It doesn't necessarily sound the same as the original lossless file (except for by extraordinary conincidence), but it can sound less harsh and more full.
And that is what happened.
that's nice, but if you didn't tell the programme to run any algorithm, it sucks too. You would expect mp3 de-/encoding to stay as close to the source file as possibl. Whether it sound like crap or a golden glockenspiel should not be the business of a de-/encoder to decide, but your own. Which mp3 encoder does your Goldwave use?