I've written previously that I think the Luneau video may be the new Rorschach test. John Fitzpatrick of Cornell used the word "crummy" to describe it, and we agree on that point. I don't know the species of the bird in the video.
With all that said, I think the bird is likely to be a normal Pileated Woodpecker. I took a look at the Luneau DVD again today, and I think the video does briefly offer a look at the bird's underwing pattern. This occurs in the first few wingbeats--you may be able to see what I mean by looking at frame 366.7 on page 7 here.
At this point, as the wing slows near the top of the stroke, the underwing pattern appears to match the upper left Pileated picture on page 319 of The Sibley Guide to Birds. In the video, the underwing is mostly white, except for an extensive black tip and what may be a thin black trailing edge. Note that Cornell says "bleeding tends to exaggerate the apparent extent of white in the wings".
The underwing pattern does not seem to match the Ivory-bill underwing pattern drawn by Sibley here. In the video, black coloring covers the entire wingtip, and the black coloring does not extend at all down the length of the underwing, as it should on an IBWO.