Its "common knowledge" that standard twist drills sometimes cut stable polygons instead of perfect circles if its a wimpy metal for the drill and a tough metal for the work (which is why woodworkers don't see this often). Thats why machinists rough cut a hole with a standard twist drill about 1/32 small then ream to precise diameter. Take something wiggly-ish thats X units long and it'll tend to catch in a corner, then sweep out a radius of X units until it slips free (and typically gets stuck in the next corner). Unfortunately this is stable and self reinforcing. Hexagons and higher order polygons are pretty rare usually you get somewhat oversize triangle-ish shaped hole. Yes the sides are not precisely flat they are curved.
So the above is a factual statement of reality. A wild conjecture is this metalworking effect might be a physical manifestation of what the OP is talking theoretically about. A further (pair of?) wild conjecture is either my example or the OPs example could have something to do with saturn's hexagon. I would not be completely surprised if there is a numerological oscillation set up where 1/6th (or 1/3rd) of a planetary rotation is exactly long enough for prevailing winds or a sonic boom or something like that to cross the diameter of the hexagon. Or we're seeing a weird phase change trick as "something" evaporates and condenses in response to a rolling atmospheric high pressure zone.
There's also a circle packing argument where at a deeper atmospheric layer than we can see, there's six rotating vortexes which just fit within the hex.
All I can say is I'm thankful its a stable 6-agon instead of a stable 5-agon or we'd never hear the end of it from the nutcases.
