Naive as in she believed him when he said the famous line: "That's my family, Kay, that's not me." She believed that because she was in love, no other reason.
Totally agree. That is the only logical answer and reason. Besides if she went for the exit,
Mario Puzo would have had to create another love interest for Mike.
My point is that I just don't think it would have happened in the real world, given Kay's background. Of course like the great Alfred Hitchcock used to say, "its only a movie".