should students be allowed to record instructors?

[Atlas Has Shrugged]

I have had some professors prohibit this. One said that she doesn't mind being audiotaped but not video (which I guess makes sense, for privacy, etc), while another banned it outright. Her reasoning was that it was her job to educate only her students, and thus if the video of a lecture winds up being disseminated by the broader public, it would be violating what she perceives to be the sanctity of the classroom.

I don't see why she would have a problem with her lectures being listened to by non-students on an audio format? If she's a poli-sci professor and we happen to be at the same barbecue somewhere for example, would she not want to talk about the subject with me since we're not in the classroom? It made no sense.