An aerodynamic stall is exactly that: the wing is stalled and is not generating enough lift to keep the aircraft in the sky. The aircraft is falling out of the sky. Whether the stall can be recovered from, and therefore the aircraft can stop falling out of the sky, is an entirely different question.
Some stalls can be recovered from, others cannot... particularly if whatever caused the stall is preventing recovery.
An aerodynamic surface which is stalled is no longer generating significant lift. Most specifically it's not generating enough lift to support the aircraft
An object which is not generating sufficient lift to keep it airborne, and is being pulled towards the earth by gravity, is falling
So yes, CNN is correct - the plane fell out of the sky while stalled. Generally a plane which is at 36,000 ft and is not falling out of the sky, doesn't hit the ground.
As Falstro mentioned in his comment, AF447 didn't realise it was in a stall at all, so therefore couldn't remove it. We don't really have enough information about the AirAsia flight to be sure what happened