More information on this unfortunate precedent-setting litigation is available on Turnitin's Wikipedia entry. I was very much dismayed but not entirely surprised by the rulings.
But I'll bet I could find a gaggle of lawyers willing to take you up on that.
If you think otherwise, lay out explicitly how you think the two cases are similar.
[1]Err, unless you are Lady Gaga.
Besides, there's obviously a difference between receiving a random essay from a person who claims to own the rights (that's obviously in their TOS), and asking to download an MP3 of some band. In the latter case, the downloader obviously knows the copy is illegal and it can be argued that (s)he's abetting the infringer.
Turnitin has always been a concern of mine; not just the copyright/fair-use conundrum, but the privacy issues too.