Bengi is full of MANPADS missiles and they thought subsequent help would be SHOT DOWN, making a Blackhawk Down/Desert One scenario right before a Prez election.
The QRF from tripoli was ambushed —what was the reason to think that the Larger and MORE expected QRF from Sigonella would not be also? This time the enemy would be MUCH betterprepared.
Their view was that they were cutting their losses.
If they had said that instead of pretending this was a sudden attack inspired by a YouTube video, they might have gotten away with it. There might have been some arguments about whether it was the right call, but nobody would be calling them liars or have a mental image of Obozo leaving Americans to die and then hanging with donors in Vegas.
Like the Rush caller described, you could have issued a C130 gunship, and then flooded a perimeter with depleted uramnm and lotsa Moooselimb unhappy campers. You could have then bought those SEALs time for friendly boots on the ground / Aviano strike / egress whatever.