QUOTE (pone @ Mar 14 2012, 12:23)

You could try:
Go to Options>Tags>Mpeg and check all three fields at "Remove"
Then test with a file the following three steps:
- copy tags
- remove tags
- paste tags
No idea if that helps.
Thank you both for your suggestions. It appears as if
ohrenkino is correct in thinking that this bit of information is only part of the iTunes database. I tried what
pone suggested, but to no avail. I have also tried opening the tags in Media Monkey, as I've heard in the past that it manages tags well. But, it doesn't show nearly as many fields as MP3Tag even.
It seems the only foolproof way to strip this information is to re-encode within iTunes (so, Right Click > Create AAC (or MP3 or whatever file type you have setup in Edit/Preferences/Import Settings - I use 256kbps AAC, which produces an .m4a file), but that comes with the very real chance of losing some audio quality, even if you're converting from filetype/bitrate to the exact same filetype/bitrate. I did a couple test files and noticed the new files, while stripped of the "Downloaded By" info, actually increased in size by 0.1 MB. Not a giant change, of course, but having a library of 55,000 tracks - 65% of which (a wild guess) were iTunes Matched and downloaded via iTunes, this would be quite the ridiculous undertaking (and an estimated increase of 3,575MB, or 3.575GB of not-new information).
Since there is no definitive way to sort by "Downloaded By" using Smart Playlists - only by manually opening each individual tag, one by one - it's probably not even worth going down that road.
Thanks again for your help and suggestions.