What may be the most frequently repeated line in the "export controls training" I received was something like "...ask your location's export compliance officer" (officer/team/department/staff, whatever the term was). All of the defense contractors, and probably every college that does affected research, have somewhere between a handful & a marching army of people who's job it is to prevent fines from being imposed on the organization. It is their job to determine if a license is needed and to apply for such licenses, BUT they do not typically go around asking people what they are doing or planning on doing in order to determine if they need a license. Everyone working on such stuff is supposed to be "trained" enough to seek guidance from the marching army when needed.
So anyone in @blueskull's position is supposed to know to ask the export compliance team to find the correct answer, not some professor who does not give a rip if the US has any advantages over its enemies. It is far better to be chided by a co-worker than to wait for the bureaucrats to discover that a violation occurred. Taking longer to get down to your level is not much consolation & from what I've seen in the corporate world they tend to start at the bottom anyway; the little guy gets punished first. Hopefully the prof. would get caught in the dragnet too, but he might get off with mere removal from the project and extra "training".
We had an instance at work one time where a guy took some stuff to the shipping department to have it sent across the border. The lowly shipping dept. person started asking appropriate questions & was able to recognize that a license was likely needed. The guy who brought the package AND the guy who gave it to him got such a swift lesson in export compliance that it scared the feces out of them, but they kept their jobs & did not go to jail or lose all their assets--because a violation was prevented.