Thanks for the welcome!
I disagree that anyone who poses an ethical thought experiment has a burden to supply a realistic amount of context—simplified thought experiments can be useful. I’d understand your viewpoint better if you could explain why you believe they have that burden.
The trolley problem, free from any context, is sufficient to illustrate a conflict between deontology and utilitarianism, which is all that it’s meant to do. It’s true that it’s not a realistic problem, but it makes a valid (if simple) point that would be destroyed by requiring additional context.
It’s easy to respond to a question that doesn’t contain much information with “It depends” (which is equivalent to saying “I don’t know”), but you still have to make a guess. All else being the same, it’s better to let 1 person die than 5. Summed over all possible worlds that fall under that description, the greatest utility comes from saving the most people. Discovering that the 1 is your friend and the 5 are SS should cause you to update your probability estimate of the situation, followed by its value in your utility function. Further finding out that the SS officers are traitors on their way to assassinate Hitler and your friend is secretly trying to stop them should cause another update. There’s always some evidence that you could potentially hear that would change your understanding; refusing to decide in the absence of more evidence is a mistake. Make your best estimate and update it as you can.
The only additional complexity that ethical questions have that empirical questions don’t is in your utility function. It’s equally valid to say “answers to empirical questions are usually context-dependent”, which I take to mean something like “I would update my answer if I saw more evidence”. But you still need a prior, which is what the trolley problem is meant to draw out: what prior utility estimates do utilitarianism/deontology/virtue ethics give over the action space of pulling/not pulling the lever? Discovering and comparing these priors is useful. The Harvard students are correct in answering the question as asked. Treating the thought experiment as a practical problem in which you expect more information is missing the point.