I can't say what is objectively true, but I can say that if I were in that situation, I absolutely would feel responsible for the outcome if I could have reasonably affected it.

If I could have done something to prevent it, but chose not to, and someone died, I would feel just as bad as if I pulled the lever and killed someone.

Statistics also won't help you with the guilt when the tram runs over 5 people and now it's just you and the one guy you saved now trauma bonded.

Actually, in this case, unless they are... refilling... the hostages each run, the results of previous runs do affect each additional run. Unless you feel that running someone over the second time kills them a second time.

I didn't need math to know that the only way I see a guy beheaded is if I don't pull the lever, so we got to the same answer.

I am not sure this is technically true if the probabilities have any dependence.