I agree that the distinction would not make the policy OK -- as in reasonable, prudent or fair -- but I do believe the legal case would be significantly more difficult if not altogether untenable. (I'm no lawyer; Cohn is, obviously.)
Surely there is little doubt that a private employer can place restrictions on the use of e-mail that would have made Spencer's 391-piece delivery a violation of company policy subject to disciplinary action.
Now make the jump from private employer to private university: Is it really that much of a leap?
Feel free to discuss.
How many phones do you have?