QXC
The position is clear.
Before any student is sent on a x/country the weather should be 100% in their favour and beyond doubt. Diversion except for unforseable occurances should be unlikely BUT PLANNED for.
The student at any time once airborne is the PIC albiet to follow the brief. The students right to make a decision as PIC must be paramount! If the student is not able to make a reasoned decision following their training then they are not ready for the QXC.
The AOPA Solo Navigation Brief form is a first class aid memoir to the instructor and student to follow.
Whatever the issues in regard to his diversion the student made a considered decision to continue on away from the fog to his next landing point. I agree with others that with the proviso the home base is CERTAIN to be clear (if not the student should not have been authorised to fly) the briefed course of action - turn back to base should have been decided beforehand if, in the event, adverse weather is encounted.
The QXC is to prove a students navigation skills and pilot proficiency in airmanship. Not completed then not done!
Yes, you do have to do it again! End of story i'm afraid.