Residency is a huge grind, made far worse when your peers aren't willing to go the extra mile to help you. It's not unreasonable to assume that the med stud who says, "My school says I can't get you coffee," will become the intern who says, "I can't follow-up on that xray because I just hit 16 hours" or the resident who says, "I can't see this consult that came in at 0600 because I just hit 24 hours." I have expressed my feelings about students over similar issues, and they did not become part of our program.
Avoiding a task doesn't make it go away, it just shifts the work to someone else. I guarantee you that once the med stud refused to get the coffee, some junior resident ended up doing it. And I further guarantee that the junior resident was far busier and more exhausted than the med stud.