I can see your professor's "point", Sanchez, but, as you stated, it has a lot of obvious weaknesses. Being in a class is more than just lecture material. Otherwise, professors would serve the same function as a textbook. Classes involve assignments, papers, assessments, questions asked after hours or by email, and official recognition of having performed to a certain level in regards to a certain subject.
It's probably more of an issue now, in the Coursera/edX era as many universities are trying to create a new revenue stream by having people pay to take mini-online courses through these platforms in exchange for a "certificate" that doesn't actually mean anything.
They don't want any lecture recordings coming out that they can't make money off of.