When you've got some kind of duty [in the legal sense] towards the person sending the mail. For example a doctor quoting a patient's email would be problematic. Just to be clear, I don't know the law in this area and I'm not saying what he did was illegal (I have no idea), I'm just saying that I can certainly see why NYU wouldn't want to step up to defend him on this issue if something came up.
I'm not sure how you can consider doctor/patient and professor/cheating student the same type of relationship. Hell, this was a 100-level class; it's surprising it even had a professor.
