I agree that Babs can be secretive and you're right that her later behavior makes the possibility that she wouldn't tell her very real. But here the question is how did she not know? Dinah and Babs drop Madison off at her school together. The story of Madison's escape would have had to have been a point of discussion. And when Dinah and Babs are reunited, Babs does not have her chair with her. It was left in Washington when she escaped with Madison. And finally when Babs regained the ability to walk it was in front of a number of people (it was a demonstration). They know who she is and there is a discussion of what happened.