Being offered the book surprises Rin, and accordingly, she raises an eyebrow. "Are you sure? I mean, if you were the one to get it for him, shouldn't you be the one to give it to him?" Of course, Vergil could simply be trying to foist the task off on her and go about his business. Were she more familiar with him, she might have voiced this suspicion, but as they literally just met, she thinks it wise to hold her tongue. You never know how a stranger is going to react. Will they brush it off? Be annoyed? Draw a weapon on her?

At least he seems to be someone Mizu trusts enough to actively seek him out, and that speaks for him. Oh, she knows Mizu himself is a killer -- but not the sort who kills without good reason, incendiary accidents notwithstanding. That's plenty enough for Rin to place her trust in him. He hasn't yet disappointed her.

Still, some basic caution is hardly ill-advised in the current situation.