In order to qualify for the fair use exception to the copyright law, the viewing must be educational in purpose (it's for a class), non-commercial (no admission charged), and shared with a limited audience (the class only). Ms. Berkeley can fulfill Professor Stanford's request with a clean conscience.
If the professor wants to teach using the video for more than the next two years, he should probably ask for permission from the copyright holder, but that would be up to him to do.