a more exact hospital comparison would be if you suppose that the power's out and you're on battery power and you have to make a choice between using the battery to power five low-power respirators or one high power life support system. that forces you to have to make a choice, and you should of course choose the five over the one.
it's not that i don't get it, it's that i think it's designed to confuse the issue, and that should be pushed back against. bringing the hospital problem in as equivalent to the trolley problem is reducing the trolley problem to a question of if you should play god or not, and that's disingenuous - especially if you don't believe in god. but, even if you did, do you think god is responsible for the situation? that would be a pretty shitty god, wouldn't it? if a god were to act like that, it would abdicate it's privileges immediately. so, i don't even want to consider that premise, i want to look at the issue as being driven by randomness, by probability, by statistics; i want to pull the rug out from under the religious debate. i just don't want to have it at all.
in the trolley problem, you're forced to make a choice and need to make it responsibly; in the hospital problem, you are not, and should not interfere.