Cart before horse. Palin has not sued; her lawyer wrote a letter raising that possibility and giving hard evidence in her favor that would be brought out in the event of a lawsuit. At the very end of the letter he tells them to contact him if they wish to resolve the dispute. The ball is in Random House’s court; they will no doubt make an offer, Palin’s lawyer will review it and negotiations will begin.
Because Palin holds all the cards, a simple apology would be insulting and will no doubt be rejected. Any final settlement involving monetary damages will probably be kept confidential but I expect much more such as public announcements that the book is being withdrawn, a lengthy statement admitting guilt and a confidential monetary settlement.
I said a “potential” lawsuit in the post!