Bai Ruozhu had suggested that those who insulted her apologize, and some judges initially thought she was asking for too much. However, after hearing what Elder Wei had said, they suddenly understood, and couldn't help but sigh, realizing they had been somewhat prejudiced.
Bai Ruozhu's demand for a public apology from her accusers was to clear the air once and for all; once they apologized, she wouldn't hold a grudge against anyone. Otherwise, if she continued to bear a grudge after they had apologized publicly, wouldn't she be slapping her own face?
Additionally, it served as a warning to those people to take responsibility for their words and to restore some justice for herself.
Of course, Bai Ruozhu also felt that the others were merely being played by Xu Panrui, Sun Lin, and the rest, and it wasn't worth harboring resentment against them afterward. It would be better to just let them apologize.