Had he done this it would have been an admission of guilt. She still would have filed a complaint, charges still would have been filed and he would certainly been convicted based on his own apology. In the legal profession we have a word for people who apologize in situations like this - convict.
BS. The main reason she filed the complaint is because a) they attacked her, called her a liar, demeaned her in public; and b) they basically dared her to file charges, implying she wouldn't file charges because she knew she was lying. A simple apology would have ended the whole thing.