Doesn't Lionsgate presently hold the distribution rights to that one? I don't think we'll be seeing it for this project.
No, The Walt Disney Company owns that special, and Lionsgate has the current video rights to stuff from The Jim Henson Company. And while Lionsgate does take down YouTube videos of material it holds video rights to, a film company would need to clear rights before using clips. Not sure if they'd need to negotiate with Lionsgate if they wanted to use footage owned by Henson that Lionsgate has video rights to, but either way, they would be paying for clearances on clips, something YouTubers usually don't do.
And I wonder, would Copper Pot need legal clearances for any behind-the-scenes home movie footage Caroll shot? I figure they'd need permisison from copyright holders for use of Sesame Street characters (but we know that Sesame Workshop has given their support, so it shouldn't be hard). Would they need permission from Warner Bros. for the behind-the-scenes footage from Follow That Bird or only if they used actual non-behind-the-scenes clips?
It is interesting that Caroll has shot so much home movie footage on the behind-the-scenes aspects of various productions over the years, considering Caroll's small salary during the early years (I imagine blank film strips would have been expensive).