It seems to me the best solution would be to have a few student workers at the university that are the plagiarism "police". They would review the TurnItIn reports for all student papers and refer offenders to honor boards for punishment.
This would leave the professor free to teach and not have to a) spend time policing the student and b) be seen as the bad guy when students get caught and punished.
There should be an automatic filter, with manual review of violations, that all papers are submitted through. If it fails the filter, it's returned to the student, and the professor hasn't even seen it. The student can redo it, or protest the automated decision, and a human reviewer (an anonymous TA on-campuse) can consider the case (and see the offending text). The reviewer would then pass it on to the professor, who can grade it, or return it to the student to improve.
This removes the burden and the penalty from the professor, whose job isn't supposed to be policing plagiarism infractions.
This would leave the professor free to teach and not have to a) spend time policing the student and b) be seen as the bad guy when students get caught and punished.