You beat me to it...this has to be the most under-reported “fact” of the entire, tragic incident. As supervisor on the scene, she could have directed the other officers to release Garner, or modify their restraint techniques. And she did neither, because (a) NYC places enforcement of the cigarette sales laws ahead of some forms of violent crime; (b) the hold used by the officer was not illegal under NYPD guidelines and (c) the supervising officer saw nothing wrong with the way Mr. Garner was treated, though her assessment is certainly subject to interpretation.
Finally, I have also heard the supervising officer was granted immunity for agreeing to appear before the grand jury. So, you can make the case that she blew it in handling the Garner arrest and when brown matter hit the rotating, air-moving device, she turned on the other officers to save her own hide.
(d) The incident happened way too fast for the supervising officer to properly react. The sergeant is not like a football referee. The ref has his eyes on the play, ready to call a foul the instant it happens. The Sgt. might have been on her radio, reacting to someone in the crowd, etc.