In the examples they show an image of a woman next to a table. The table is covered with a table cloth. In the corrupted image the table cloth looks like all noise to the human eye, however in the reconstructed image you see that the method is able to recover most of the pattern in the cloth.
That's something different: a demonstration of an "inpainting" problem. The black pixels were specifically marked as corrupt. Also, the pattern on the cloth is much less granular than noise.
We need more than just the information where corrupted pixels are.
For example, consider an image of a woman, severly blurred such that her individual fingers cannot be discerned but you can still see that it's a woman. A "learned" context-aware approach can now deduce that the "blob" that is her hand should be inpainted by fingers. A non-learned approach can't do that.
