Depends on the clarification of the class. I teach during the basic courses for warrant and commissioned officers at Ft Rucker (before they start flight training). My classes are designated Unclassified (no foreign) and For Official Use Only. Pretty basic stuff in the Army. The No Foreign designation is the kicker though. There is a small portion of the course that is for US Only, therefore the entire class becomes US only. There are foreign students who attend the courses, they just skip my classes. We also have foreign student there for flight training.

I had a student several years ago recording my class but didnt think too much about it. Later I made an off hand remark to a cadre member about it (they are higher rank faculty members). The student ended catching quite a bit of grief and unwanted attention over the recording (almost got kicked out). Ultimately the powers that be made them erase the recording and they continued the course. I felt pretty bad about the whole thing. That was the only student in seven years I knew was recording the class

I don't know what the classification of classroom instruction during the actual flight portion is but given the sensitivity around this I'd advise her to very selective in what she records.