Rereading this, after Izumi's first appearance before she introduced herself was kind of shady I'll admit, but afterwards, her reactions are totally normal and matches with the author's intentions here. It's normal to blush in her type of situation (especially romantic-like but doesn't mean you hold it) and her talking about Eiji, she just explained that she wants to keep their friendship and that means not make him feel like a third wheel even if he's not there.