But this series of even that happens make it more likely to happen. First Uraha join the household, later on Onee-san went back to home, maybe Uraha gonna remind her about the old Uiha like how everyone else react, remembering the past makes her airhead self slipped out about how our MC is an adopted child (Maybe she say stuff like "He is also pretty gloomy when he first arrive to our household himself"). And then BOOM, the tea was spilled...
I mean, she is an airhead, that doesn't mean that she would forgot stuff about her own family.