At this point, having read the entire thread, it seems we're just going around in circles.
The problem manifested itself for me with the ATV OS 6.0.1 update a few weeks ago. That's also about the time that I noticed the "Super HD" badge on a lot of shows. I just thought it was some marketing gimmick on Netflix's part, because everything looked HD to me before, so what the heck is "Super HD?"
I only updated to ATV OS 6.0.2 a couple of days ago while reading this thread.
I don't watch any of the popular shows (I mostly watch documentaries, older shows, or independent titles), so I don't think the problem is that there is overwhelming traffic to a super popular title I may be watching. I also don't think it's time of day.
So, my conclusion (and it seems the conclusion of most of the thread participants) is that something is not right with the Netflix app included with iOS 6.0.1 and 6.0.2 that needs to be fixed. Like everyone else, I have no problems playing HD content from other ATV apps.
In any case, like someone else mentioned on the thread, I've discovered that a workaround is playing the desired Netflix title on the iPad (iPad 3, iOS 7.0.4, Netflix 5.0.2), and AirPlay it to the Apple TV. We watched three documentaries that way last night (Thanksgiving), and they all looked great. Maybe it was because most Americans were watching live football or something, but we were happy to watch something on Netflix in HD again after suffering through bad pixelation for days.