It’s not “some body,” it’s actually the cloud layer of Saturn. And yes, you wouldn’t need a pressure suit at that location, just oxygen mask and cold weather gear because the pressure at that point (400 millibar up to 4-10 bar) is Earth-like! The author of that video was, in fact, intentionally using a fur lined coat/hood/hat to underscore the fact that the pressure is Earth-like at the Saturn cloud layer and the coat is not a pressure suit but just insulation.
So it was intentional and accurate (or, rather, a possibility), not an unscientific mistake.