Any aircraft can fly itself. Automation in flight systems is not new nor does it even require a computer. Negative feedback systems in both machines and in biology can do it very well -- in insects and birds it happens beautifully.
Early autopilots were analogue and worked remarkably well. Drones can keep flying and gliding without help (as long as they have power and fuel) -- of course they can. Its a classic and ancient application. But right now that makes them one step above a paper dart -- all be it with weaponry and reconnaissance. And that don't work without human intervention.
They are merely a remote extension of their human pilot's hand. Thankfully, because no one wants an autonomous drone going off on its own to "discover itself".
The ability for a 'pilot' to specify they want surveillance of some area and a drone fly's around pointing a camera at that area is a little more complex than simple autopilot. Classic reconnaissance aircraft often had multiple people to handle all of the complexity's involved, moving to having less than one person per plane and doing the same job takes a lot of automation. That said, something like the MQ-1 Predator actually uses multiple people on the ground due to this issue as does the MQ-9 Reaper which can do autonomous flight operations. But, both systems use multiple aircraft at the same time and have less than one controller per aircraft.
The key word is optionally piloted http://bayourenaissanceman.blogspot.com/2011/05/more-about-f...