The lawyer will refer to it as intellectual property....just like copying movies or a favorite song without permission.
The property belongs to the purchaser that is the tuition paying student.
What is a college course, if not an agreement to share intellectual property for consideration? How can the party to the contract agreeing to share intellectual property restrict the use of it, if the party with whom said intellectual property was shared expects to benefit from it, in employment and social advantages? They can't, not without destroying the foundational reasons behind seeking and paying for a college degree.
Well, the student does pay for the course, so why can’t they record if not otherwise specified. I also believe that this was a public institution, so the professor as an individual would not have the copyright.