This is only partially true, though; a totally flat wing can also support flight. The shaped nature of the wing contributes to its efficiency (and other factors) but do not make other wing shapes incapable of supporting flight.
The reality is that the Wright brothers' innovation was not the airfoil shape or even the lightweight motor. It was the control surfaces, to allow the operator to adjust the plane's attitude on the three axes of rotation, allowing actively stabilized flight.
Paper airplanes and kites demonstrate all the same principles of heavier-than-air flight (the Wright brothers even had a kite version of their airframe they used for testing), despite the fact that they generally do not exhibit shaped airfoils.