Let me quote two paragraphs from p. 226 of Bamford's Body of Secrets:
At 11:29 A.M. (5:29 P.M. Liberty), [Lyndon] Johnson took the unusual step of ordering the JCS to recall the fighters while the Liberty still lay smoldering, sinking, fearful of another attack, without aid, and with its decks covered with the dead, the dying, and the wounded. Onboard the flag ship of the Sixth Fleet, Rear Admiral Lawrence R. Geis, who commanded the carrier force in the Mediterranean, was angry and puzzled at the recall and protested it to Secretary McNamara.
Admiral Geis was shocked by what he heard next. According to information obtained for Body of Secrets, "President Lyndon Johnson came on with a comment that he didn't care if the ship sunk, he would not embarrass his allies." Admiral Geis told Lieutenant Commander David Lewis, the head of the NSA group on the Liberty, about the comment but asked him to keep it secret until after Geis died. It was a promise that Lewis kept.
So, while Cristol's claim may technically have been correct (the order came from LBJ, not McNamara,) the overall effect of his presentation was deceptive. Not for nothing was Cristol trained as a lawyer.