That's a perfect reason why JJ blew out all canon. It didn't make any damned sense. I can't believe that the command staff of the flagship of the Federation (the ship tasked with highly delicate job of Klingon diplomacy) didn't know a damned thing about the Klingons. It would be like the chief of protocol at the State Department in the 1980s not know anything about the Soviet Union. As far as not knowing anything about Klingon anatomy? Even ignoring the retconning job Enterprise did...there wasn't ever one Klingon corpse found by Starfleet in the past 100 years? Even if McCoy didn't personally dissect the body, his professional curiosity should have forced him to read a damned book on the matter.