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?
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!