Uh...did you miss the part where the two girls speculated that that what Alice really meant was that she says he's always hanging around her despite her lack of interest but she just won't leave on her own (which she certainly could do). That resulted in her blushing with a verbal denial (tsundere), confirming that she is the one deliberately continuing to hang around Liszt, which for some reason that would be embarrassing to her. This goes along with the initial question the girls had about the two of them going out, and the concluding remark that he will, "keep pushing back the wedding date."
And the accuracy of two girls' intuition is confirmed by our Narrator.