Pretty much the chance you have to take if you are going to rapidly ramp up an efforts that requires large numbers of people fluent in languages little spoken by older immigrant groups. It would not surprise me to learn that various government agencies were willing to overlook questionable immigration status to recruit such personnel.
Is my reading comprehension low this evening - or did this article not mention if she was a Muslim? Understood she was working at a restaurant owned by a contributor to Hezbollah, and Hezbollah is a Shia Muslim organization, but what is her religious affiliation? The reason I think this is a critical missing ingredient is that the proper fear in this situation is the possibility that you can take the Muslim out of the Middle east, but you can never take the Muslim out of the Muslim, so to speak. My limited reading on th is subject(a couple of Bernard Lewis books on Islam) tells me that there is no jurisdictional component to Islam - you are the same regardless of where you are on the surface of the earth (i.e., not an American, a Swede, an Angolan, etc.) and I think we may have much more to fear from this combination of alliance only to Islam and our piss poor internal security procedures at CIA/FBI/DHS/you-name-it.
OBTW - note her entry into the FBI was during the Clinton Administration. That was hard to miss.