I've shot my latest film on the 5D3, IMHO the video quality is noticeably better than the 5D2, particularly the noise when pushing the ISO past 800.
Judging video from a still is the wrong approach, also judging video that was shot incompetently vs. video which was properly lit and exposed is also not a way to judge a camera's capabilities.
Lastly, noise in video is generally much more accepted by the public than noise in still photography. I watch so many DVD and Blu Ray big budget films which look pretty sad in the shadows and darker scenes noise-wise...yet I don't hear many people complaining about how bad the film looked.
Absolutely, but the Mark II and Mark III produce very similar footage (excepting aliasing issues) at low ISOs, with the Mark II arguably having the edge slightly for sharpness (due to false detail) and having a bit less read noise. At high ISOs the Mark III is far nicer, but this isn't that.
Again, the footage posted above is WAY worse than what the Mark III is capable of, and it's also under the conditions that are least impressive with the camera. But the crop taken from a still is better than the camera will ever produce for video.