Surely in the contract that the school signed they gave TurnItIn permission to use these data in this way, and asserted that the teacher, by uploading the document, is ensuring that he or she has the right to grant that permission. At the very least this pushes the IP issues onto the school, as far as TurnItIn knows they have every right to use this content in that way.
It seems probable that the admissions paperwork for the school probably granted the school the right to make limited use of the work the student turns in. I know when I had to complete a "Bachelor Thesis" the school retained the right to use that content, at least for publication and probably for sale if they chose to. Is that uncommon?
Also, I think the problem TurnItIn is trying to solve is less about copyright violation and more about plagiarism/intellectual dishonesty in an academic context. You could readily buy a paper or essay from someone to obtain the copyright permissions, but if you submit that as your own work to the professor you've violated academic ethics.