What I think this best demonstrates is that, in addition to everything else, the muppeteers were really, really good technical puppeteers. The muppets movements are absolutely natural and the puppeteers are invisible. These people were good.
The thing about puppetry, however, is that the audience is WILLING to ignore technical flubs if the performances and story are engaging enough. Japanese puppetry is one such example, they think it's weird that we try to hide the puppeteers.