A cruise missile is unmanned yes. But it is not an UAV per definition: "An unmanned aerial vehicle (UAV), commonly known as a drone, is an aircraft without a human pilot aboard." For the discussion at hand it does not matter that much.
There is a difference between 'unmanned' and 'unpiloted'.
In flight, if the pilot is somehow incapacitated and there is no one to assume control in the same capacity, the aircraft is essentially unpiloted, even if there are other people on board. Unmanned does not mean unpiloted. Unmanned can also mean remotely piloted. An unmanned aircraft can be designed to be remotely piloted no matter what, it means if without constant inputs from that remote pilot, the aircraft will enter uncontrolled flight.
I am guessing that what you are pointing to is the fact that the stability control of the aircraft is autonomous. Yes of course! It could most probably fly routes without human interaction as well. However I would be surprised (in contrast to cruise missiles) if the drone does not get any signals from a pilot/operator/"whatever you want to call it" while performing its operations.
Flight control stability is not operations, course, and mission autonomy.
Modern flight controls have high, and increasing, autonomy. It means that flight operations are within the aircraft's own programming, removing much of the flying burdens from the pilot, whether that pilot is on board or remote. Flight controls stability fall under operations autonomy.
Course and mission autonomy are where things can get confusing for lay people. Course is simply going to point A to point B. In this, UAV, which includes the cruise missile, can and do have high degrees of autonomy. The mission, or the goal, is where the remote pilot is needed. For example, if the mission is observation only, then the UAV can be mostly autonomous, from take off at point A, to flying a path to point B, to assuming an observation flight path at point B. There will be minimal human interactions even at point B. On the other hand, if the mission is to deliver a weapon at time unknown, then at point B, human interactions will be maximum.
I don't know if that was the answer to your somewhat fuzzy question. In either case please make your point with whatever base conditions you need.
The bottom line is that this statement...
Bearing in mind that flying wings are notoriously difficult to keep in the air and need constant FBW input just to keep them from going out of control.
...Is technically wrong.
The flying wing design is problematic in the yaw axis, but that is solved decades ago. There is a false assumption that
'constant FBW input' means human inputs. The reality is that the fly-by-wire flight controls system removes the human pilot from that problem, at least with US designs anyway. What this means is that if human pilot inputs are absent, the flying wing UAV will revert to programmed responses, whatever they are. But it does not mean the flying wing UAV will enter uncontrolled flight, crash, and there is a wreckage of aircraft parts on the ground.
