Poitras is actually the shadow of this whole story. She was the journalist Snowden reached out to when Greenwald was unresponsive, was there and filmed the first Snowden interviews, was responsible for the Bill Binney story in the NYT a few years back[1] and has been on the US Government shit list for quite a few years[2].
I think you might have misread what the gp meant by "tasked". It was taken directly from the video. In the video "tasking" meaning being selected, followed (presumably virtually only), monitored and spied on.
And she was the one with a safe copy of the NSA documents once Greenwald disovered his copy was corrupted. That's why David Miranda went to Europe and was detained at Heatrow.
[1] http://www.nytimes.com/2012/08/23/opinion/the-national-secur...
[2] https://en.wikipedia.org/wiki/Laura_Poitras#Government_surve...