Obviously the woman didn't have as much of a clue as she thought she did. Hermione's forced politeness had nothing to do with Divination and everything to do with her occupation. While she didn't care to practice the subject, she knew there were times when Divination could be valid.
Were she not already miffed that her research had been interrupted, Hermione might have told the woman just how wrong she was. Instead, she simply nodded then returned to her work.