The kids are right in one aspect. If they submit the EXACT same paper that they submitted in 10th grade to a 12th grade teacher, it is my belief that the system would say they stole it. However they certainly didn't. It is and always has been theirs. I know I personally "reworked" a good paper I had for about 3 different classes in college.
However I am not certain if that would be "copyright infringement" until the company in question made money by showing that document to the school in question. In other words if they submit the paper and the turnitin.com reports back that the paper was not original and then showed the paper (in part or full) in comparison to the original paper, and fails to cite the proper source (and obtain permission from that source) then yeah... I think there is infringement.
Whew... I am tired.