Philippa Foot is most known for her invention of the Trolley Problem thought experiment in the 1960s. A lesser known variation of hers is as follows:
Suppose that a judge is faced with rioters demanding that a culprit be found for a certain crime. The rioters are threatening to take bloody revenge on a particular section of the community. The real culprit being unknown, the judge sees himself as able to prevent the bloodshed from the riots only by framing some innocent person and having them executed.
These are the only two options: execute an innocent person for a crime they did not commit, or let people riot in the streets knowing that people will die. If you were the judge, what would you do?
This is even worse logically than the premise of the Trolley problem. You're basically reframing a terrorist or criminal holding a gun to a bystander's head and demanding something trying to say it'll be my fault the person dies if I don't give them whatever they ask for.
No. It's got nothing to do with me (or the judge). The criminals threatening violence are the bad people.
The only good "Trolley problem" rewrite I've heard is the crying baby and the hiding refugees. https://www.truthorfiction.com/crying-baby-ethics-question-causes-viral-controversy/
All the others are either too contrived (how did those people get in the trolley tracks? why is there no driver? why am I able to get to the lever or how do I know a fat man will detail the trolley?) Or it's just a terrorist blaming someone else for his actions. The crying baby one challenges me on a very deep level.
I think you're being a little too quick to judge (no pun intended) by dismissing these scenarips as assigning blame. The point of these problems isn't to decide whose "fault" it is or who is the "bad guy" - they are thought experiments to explore what is "right" to do, according to various schools of thought.
In the original trolley problem, or in this one, it's totally fair for you to say "whatever happens, it's not the chooser's fault - they were forced into this position, and so they cannot be to blame". That's fine - but even if they are absolved of blame the question still remains of what is right for them to do. If your answer is "whatever they want (because engaging with terorrists' demands is always wrong)", or "whatever is the opposite of what they're being pressured to do", or "whatever is the least action", or "whatever rminimizess suffering", or "whatever minimizes undeserved suffering", those are all still answers to the question, without any implications of blame or guilt to the chooser!