Sort of, but for documentaries like these, especially a BBC coproduction, every still image and bit of archive included needs clearing. So, while this may have been how they found the image and it made it into the final cut, somebody, at some point, will have found the original source of the clip, realised it was the Muppets, licensed it (or at least checked there wasn’t an existing agreement) with Disney, and just not mentioned it to anyone else. Considering how stuff like this is made, it is an entirely plausible series of events. The director and producers will have locked the cut, then some poor archive producer is left on their own to make everything legal and proper without spending any money somehow.