You're really over thinking this. The classical problem is more or less designed to be a utilitarian thought experiment. Are you willing to be actively unethical for a greater ethical action? Are you willing to be passively unethical to allow a greater ethical action to happen? Is it possible to be passively unethical?
There is enough philosophical meat in the thought experiment without going "out of bounds" and trying to undermine the question. Your comment would make for a good modern essay, but it frankly dismisses the spirit of the problem.
Good faith arguments in philosophical debates require both parties to have a common set of premises. If you don't both work from those premises, you need to go "down" to your next set of shared premises and start arguing "up" from there. If you don't do this, you're just talking past each other and you end up in a Wittgenstein-ian limbo where each of you is arguing coherently but disparately and no one is going to take the other's point.
Given this, it's not a good faith argument against the trolley problem to say that an action doesn't make sense due to premises that are not typically included in the classical problem.
Furthermore, the only reason we have thought experiments like this is because it is difficult to reason in the abstract without formal training. Using concrete allegories helps to give participants mental "skin in the game" to illustrate whether or not their opinions are coherent.
Allow me to restate this problem: "Given a simulation where you have the choice between certainly observing five people die by taking no action, or certainly saving five people by taking an action that certainly kills one person, and all persons are equally familiar to you, what do you do?"
Now, a valid response is to disagree with my problem as stated. That's fine, but then we need to argue something else because we're no longer talking about the trolley problem as it is classically defined and intended.