I think perhaps Tsugumi wasn't told everything. Near the end, they all looked like they were ready to kill Shu. Would Tsugumi really agree to help or not intefere them if she knew that Shu's death would be the final part of the plan?
One thing is for sure, none of the students (Except maybe Arisa) knew that Gai and some others were going to turn up and slice Shu's arm off.
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