I don't think this was live at all. You can tell especially because the guitar strums are very off in a lot of the shots but none of the other audio is off. Which means they recorded it and when playing the guitarist didn't use quite the same strumming pattern for the video in which he did in the recording.
Most bands do this and most companies/video makers that do acoustic videos like this do it as well. The performance is incredible but it's clearly EQ'd a ton and tuned up quite a bit.
i think its just that the audio is out of sync with the video, which happens all the time on youtube. sure its possible that this audio was edited, but Nate has always been that good live, even way back in the format days.