In terms of morality, the notion always talks about right/wrong, thus speaking of absolute values. What I feel is neglected though is conscience. To me, letting 5 people die is wrong but so is sacrificing one person. I will feel bad either way and both choices are wrong, but one feels worse. So, while principles speak in absolutes, many of our actions are based/weighted in relatives which, imo, allows us to act ~consistently with our moral views.
Similarly, some might say that to maximise happiness is a "stronger" (more important) principle than not killing anyone. Therefore, I think it's wrong to not mention priorities.
So yeah, to me, the trolley problem ignores the important role of conscience/priorities.
And finally, morals are a human concept imo. We aren't obliged to do or follow any rules, it's just better to have some (for survival/societal reasons).
You have 2 interesting claims here:
1) You claim that both choices are wrong and I presume you are using wrong in the "morally invalid choices" sense of the word (because that is the sense that the trolley problem uses the word). When given all of the choices available, it make no sense to claim that none of the choices, including inaction, is a valid choice.
2) You claim that the trolley problem ignores the role of priorities. Since the reason for the various variant formulations of the trolley problem is to identify and isolate various morally relevant factor, it is trivially true and yet technically false to say that it ignores priorities. It is true that you are ignoring other factors when you consider 1 factor
while holding all other factors constant but it is trivially true. However when you combine these isolated comparisons and the less isolating comparisons it quickly becomes apparent that such questions do take priority into account.
While part of this is answering a different question than what was asked, I think that another part of this is going off the linked article which only contained 4 variants although those variants did include one of the valuable differences. So to fix that here are some more variants:
Group 1: There is an unmanned Trolley with 2 routes controlled by a track switch lever. The default path contains 5 people and the alternate path contains 1 person.
Var 1: You are at the track switch lever
Var 2: You are one of the 5 and are at the track switch lever
Var 3: You are the one and at the track switch lever
Var 4: You are at the track switch lever and the 5 are close friends/relatives of yours (answer for each group that has a morally relevant difference)
Var 5: You are at the track switch lever and the 1 is a close friend/relative of yours (answer for each group that has a morally relevant difference)
Var 6: You are at the track switch lever and the 5 should have known better (common example used is them being trolley track workers)
Var 7: You are at the track switch lever and the 1 should have known better (common example used is them being trolley track workers)
Group 2: There is an unmanned Trolley with 1 route that contains 5 people. The Trolley AI will instantly stop if Bob dies. You can kill Bob with your gun.
Var 1: Bob(someone random) is standing next to you.
Var 2: Bob(someone random) and you are two of the 5.
Var 3: Bob(someone random) is one of the 5 but you are not.
Var 4: You are on of the 5 but Bob(someone random) is not.
Var 5: Bob(the Trolley controller) is standing next to you.
Var 6: Bob(the Trolley controller) and you are two of the 5.
Var 7: Bob(the Trolley controller) is one of the 5 but you are not.
Var 8: You are on of the 5 but Bob(the Trolley controller) is not.
Group 3: There are 2 unmanned Trolleys. One is set to hit 5 people and the other is set to hit 1 person. You have time to stop one, the other, or neither.
Var 1: To stop a Trolley you must kill Bob or Jane(someone random)
Var 2: To stop a Trolley you must kill Bob or Jane(the Trolley controller)
Var 3: To stop a Trolley you must flip a track switch lever
This is nowhere near a complete list of variants however it should, with someone's answers, show how the isolated and aggregate questions work to demonstrate the moral rules the person is answering by.