I don’t think we had a CVN in the MED at that time.
IIRC, the story about Rear Admiral Gaouette (Sp?) being relieved of command of the group broke just after Benghazi. Speculation was that he refused to stand down from launching a rescue, not the story about "sending racially insensitive e-mails to white officers".
The Chief of AFRICOM (General Ham) got changed out at about the same time (just after Benghazi).
Maybe it only seems like a lot of flag rank reassignment at once for an area, but added in with Petraeus, Pannetta, and Hillary's exit, there seems like more to the picture than just a few folks changing jobs.