Apple TV won't start Netflix Streams
So I took the first ATV back to the Apple Store, and had a repair by replacement. It still had problems, so I started digging deeper.

Through some more specific testing, I narrowed down that it was only happening with movies that had Dolby Digital. In the settings, I had forced the Dolby on in the settings. Turning that off fixed it. It is still stable with Send data to Apple turned on, and switched back over to Google DNS.