The CIA uses the FIB for security?
armed with a flag.
More likely than not, since it was an hours long standoff in the DC area, the FBI had someone dispatched to the scene but it's really unlikely the CIA headquarters doesn't have a whole lot of armed police with federal law enforcement authority. Regardless of who actually shot, the FBI probably agreed to take the "heat" on this shoot because the paperwork is cleaner and they'd do the follow on investigation anyway.