That one was raised by a visiting philosopher at my college as an argument (from intuition) against utilitarianism. I pointed out that if we tended to kill patients to harvest them to save more patients, people would be so fearful of being harvested that they would tend not to visit hospitals at all, leading to a greater loss of health and life. So in this case, in any realistic formulation, the less comfortable option is also the one that leads to less utility.

I suspect that this version feels even less comfortable than the trolley dilemma because it includes the violation of an implicit social contract, that if you go into a hospital, they'll try to make you healthier, not kill you. But while violating implicit social contracts tends to be a bad idea, that's certainly not to say that there's any guarantee that the utilitarian thing to do in some situations won't be massively uncomfortable.