Remember, Obama has taken great pride in saying that Libya was liberated without American blood being shed. Obama did not want potential voters to wake up to our uniformed military being KIA.
So, DOD assets were told to stand down as CIA subcontractors, whose presence could be concealed, were tasked with extracting diplomatic assets from the Mission. Also, those operators were familiar with the battlefield and were leveraged with local friendly militia.
As the battlefield was so unshaped and on/off and populated by hostiles of unknown strength and unknown weapons, this was a reasonable tactical choice anyway.
Other rapid response units that could have gotten there would have been too little and too late.
General Ham and Africom, were frustrated that in this theater of their responsibility, they were not in position to act effectively.
Sigonella and Tripoli are roughly equal distance to Benghazi. This was a totally political decision not to involve the US military in a trans border operation.