That's... actually a pretty healthy attitude to have about people suffering from delusions, if imperfect. The general best advice is not to deny someones reality- mind, in the case of someone who doesn't have dementia, re-enforcing it isn't great either. In a case like that, not just telling them "um thats not true" is good, mind. But you don't go "yes you're right about X". Usually what's emphasized is finding steps to help someone feel safe. If someone feels/sees bugs crawling on themselves, ask if borrowing your jacket to wrap their bare skin up could help. That kinda thing.
That being said, for a teen girl w/o any particular training, who isn't directly responsible for the well being of our "isekai" gal, I think she handled it very well! Using her experience with her grandmas dementia is very smart and kind of her, imo.
Also for why everyone else thinks she's rude... I feel like her desire Not to Cause Trouble combines really badly with the way it's indicated she speaks in japanese. Probably comes off as 'putting on airs'.
tbh even in america I think if your group partner said "My Good Fellow Student, I mind not what we procure for our ardent Task" you might wind up not super popular.