If the faculty member decided that the use was not fair and therefore she had to ask permission and the owner says no, that's the end of it.

On the other hand, if there is a reasonable argument to be made that the use is fair, and she was asking permission to be on the safe side (since fair use is always somewhat nebulous), she can still rely on fair use even if the owner says no. She should be very sure of herself in this instance, however, because she may very well be challenged regarding the use.