I don't have the patience to listen to this guy for very long, but I noticed that he was very interested in lining up two of the patterns when they looked very similar, but as soon as there was a big difference, he moved on to something else, without acknowledging it.
Two points here:
One; Henley has been performing this song for about 50 years. It wouldn't surprise me at all if two different performances sounded exactly the same.
Two; If he was going to lip sync, why would he choose a recording that sounds like that?