Well to be fair Tsumugi Spica is already acquainted to that former detective. I'm pretty sure her coworkers in the cafe saw her plenty of times talking to that former detective and some nurses saw her visiting him in the hospital before he passed away as well. To be honest there's really no reason for this to become a big deal at all. Maybe they should just think he wrote that because she was the last person who visited him before he passed away.