My friend is a PhD student in the "Jessica" computer science lab. Before beginning, he and Dr. Jessica came to a verbal understanding that he'd be allowed to graduate in time for a job offer scheduled to begin a few years after starting the PhD, but only if he passes his prelim and completes drafts of research papers covering all aspects of the prelim. No written records of Dr. Jessica's agreement exist, as Dr. Jessica was careful to organize only face-to-face meetings about this.
Dr. Jessica has reneged repeatedly on her promises and keeps upping the ante for graduation -- from having manuscript drafts to submissions and now to acceptances. Meanwhile, my friend has no written record of this and doesn't know what to do despite his job's start date closing in. He is not even allowed by Dr. Jessica to bring up the topic of graduation with his committee without her consent. What, if any, recourse does my friend have?