The account was shut down due to certain people reporting it for copyright. I've sent emails to try to correct this but can only call this a major loss. Much of what was on the channel consisted of new restored edits unavailable elsewhere.
Some of the Henson Rarities material is on Vimeo but very little.
https://vimeo.com/user915081/videos
As for Secrets of the Muppets, like much of the content on Henson Rarities this was an original restoration by myself which took some work [and which I never officially finished]. I was replacing many of the clips with higher-quality material from DVD and so on.
The actual source for the episode I don't know much about, but to my knowledge it's not from any broadcast; it's the correct, original version of the episode as prepared for The Jim Henson Hour. For instance, "Couldn't We Ride" and the commercial breaks display the Jim Henson Hour logo, which I approximated in the edit. Nickelodeon obviously made some changes for their purposes. I seem to recall there are no commercials on the tape, just black screen.
The low quality versions of "Food" and "Living With Dinosaurs" that circulate are similarly not from broadcast, although the non-Jim Henson Hour versions that we dug up are [including some high quality copies of "Dinosaurs" and "The Jim Henson Show: Food"].