Okay: Results of the tests:

Mark's supplied MP3 files from his collection:
- Mark's 44.1k file: Good: No distortion.
- Mark's 48.0k file: Bad: Distortion.

My files:
- Original 48.0k file: Bad: Distortion.
- Convert Original file to 44.1k: Good: No distortion.
- Convert (redo) that 44.1k file back to 48.0k: Bad: Distortion.

(By the way, my command lines for the back and forth conversion I described above were:
sox.exe Lincoln48.mp3 -C 360 Lincoln44.1.mp3 rate -v 44.1k
sox.exe Lincoln44.1.mp3 -C 360 Lincoln48redo.mp3 rate -v 48k
Also, I checked all files in Winamps "file properties" box and made sure it agreed with the sample rates, and made sure that the track names were carefully tagged so that I could tell for sure which one is which during playback on the Empeg.)

So it's definitely a problem that is specific to the sample rate, and it is not a quirk of the encoding. It's also definitely not a bitrate thing, because on my files I was working exclusively at high bit rates (now that I know the Sox command line for it), and Mark's files were at 128k.

Mark says he couldn't hear the difference in the files he supplied, but I could hear it. It's a subtle difference, and I'd only say the difference was "clear" at certain points in the songs where there was content which made it obvious (in this case a solo female voice singing open vowels). But at those points the distortion was clear as day to me, but I could see how it would be subtle to pick out for some folks.

There's also the possibility that there's a difference in firmware or hardware on Mark's empeg from mine, and that the version he's running is better about 48khz playback.