Yes. The crushed pills in the liquor would have been enough to kill her. There was no need for a cut in her arm. Not only that, the note specifically mentions 'pouring one out'. If a third party faked that note, then why'd they make a cut in her arm, too?

Besides, I also remember it's a fresh wound. When the body was found, the blood was flowing, right? It's a wound that can only have been made when she was alive -- blood doesn't flow so easily when you're already dead.

Finally, it's not like the body was hidden away. Someone would have found Eide-san sooner or later. It's not like the blood was needed to alert us she was dead, we'd have seen that sooner or later -- if Jericho didn't tell us about it, of course.

[She shrugs]

Do you see what I mean? No matter how you look at it, that cut is nonsensical.