Think about it: what good would it be to the doctor to lose your life to save someone else’s? You are both patients, he wants to save you both, so exchanging one for the other does not make sense. (No, he does not get paid for your organs, obviously.)
Nitpick: Hippocratic Oath is not in general use anymore, though similar, more modern codes of ethics are. (Hippocrates had in his stuff like not doing surgery or abortions, not to mention a heavy implication of only teaching the art to males.)