Why the need for context? It was easy to see she was blaming Benghazi on the video, irregardless of the five other attacks.
It's only "easy" to see that if that's what you really want to see.
Seriously, let's take a close look at that quote.
This has been a difficult week for the State Department and for our country.
This implies that more than one event has happened in the last week.
We’ve seen the heavy assault on our post in Benghazi that took the lives of those brave men.
That's one event...
We’ve seen rage and violence directed at American embassies over an awful Internet video that we had nothing do to with.
...and that's another event.
“I myself went back and forth on what likely happened, who did it, and what mix of factors— like the video— played a part. But it was unquestionably inciting the region and triggering protests all over,
so it would have been strange not to consider, as days of protests unfolded, that it might have had the same effect here, too. That’s just common sense. Later investigation and reporting confirmed that the video was indeed a factor. All we knew at that time with complete certainty was that Americans had been killed and others were still in danger. -Hillary Rodham Clinton,
Hard Choices, 2014