You can always tell when a lawyer is lying because they resort to semantics to wiggle out of questions.
Maybe they didn't deny it but they didn't approve it either.
Or maybe the WH had someone else deny it.
Ding, ding we have a winner. They didn't issue a denial of assistance, they simply didn't approve the request of assistance. I really think this whole thing is on Valerie Jarrett. She was afraid of sending in the military in case there was a Desert One/Black Hawk Down type incident in an election year. So she sacrificed the lives of everyone in the consulate instead.