True, but which kind of acceleration are we talking about?
A cat in the "zero g" in the experiment described in the video has no coordinate acceleration relative to the Earth. Whereas a cat falling off a ledge to the floor does have coordinate acceleration relative to the Earth.
But both cats have zero proper acceleration--they are both weightless. (Air resistance will become significant at some point during a fall from a height to the floor, but cats are heavy enough that I don't think that would be significant in most falls where cats are observed to land on their feet.) And "zero g" means zero proper acceleration, not zero coordinate acceleration. So the GP is correct and my original comment was in error: cats in both situations are in "zero g" so that can't be what is causing the different behavior in the two situations.
There is no such thing as a stable orbit “at sufficient distance to not be influenced by” gravity.
There’s no such thing as a sufficient distance.
I guess certain multi-body situations like Lagrange points might make it debatable about which "direction" you're falling though.
The GGP didn't say zero-g "is" falling. They said it's "the same as" falling. Which, for purposes of this discussion, it is, for the reason I gave--the key common property is being weightless, i.e., free falling.
Note, btw, that "free-fall" does not necessarily imply "downward acceleration". It just means "weightless". You could be weightless, in free fall, far out in deep space well away from all gravitating bodies, so that there is no well-defined notion of "downward acceleration" in your vicinity.