I have seen nothing from Palin’s lawyers in the public record suggesting they think attorney-client privilege is the issue. It certainly is not in their letter.
If you have a private communication with her lawyers, then you have better information than the rest of us. If you don’t, then I don’t know where you get this idea, because i don’t see it in the public record.
Communication between a lawyer for a firm and an outside party would not be protected by any privilege; The e-mail they have from the author gives evidence that the author received e-mails from the firm that suggested they knew his charges had no factual evidence, and that is what their letter to the firm references. Not A-C privilege.
It’s in their letter to Random House —I suggest to reread it