I can't speak to the other place, but at Oxford the system of "exams" ("responsion to the question" for undergraduates, "determinations" for bachelors seeking to be admitted as masters) was not the kind of thing that seems possible to me that one could cheat on, involving as it did a viva voce panel examanination (in Latin, of course). Moreover, for those students with perhaps more money than brains there was a separate process by which one could receive a degree without going through this process so long as your studies were sufficiently lengthy.

That being said, in cases of misconduct the Chancellor of Oxford was not merely the chancellor of the university at this point, he was the chancellor of Oxford as a city. As such he wielded the full judicial powers of the state and through the chancellor's court could do everything from issuing fines to imprisonment, in addition to academic punishments like the stripping of degrees.

For more on this have a look at The History of the University of Oxford: Volume I: The Early Oxford Schools