I have yet to find any normal situation where the 5D3 won't focus in low light. For what the 6D is capable of would almost be too dark to really be shooting anything, at least you won't have any real color to speak of. I know the 6D focuses better in lower light, but after reproducing the light levels they talk about for the 6D, I would never shoot in those conditions.
This is about as low as I go, this is how the scene actually looked, there was barely any light on the troop here, and the 5D3 had no issues locking on.
Ya the 6D is ridiculous at how low it focuses. Literally it's focused on crap I cannot see. The 5D3 is only -1ev off. Much better than the -.05 rating of the 7D.
But like you said you get into light this low and results are blah at best.
Your photo is EV4 by my calculation or close to it.
This nothing special shot was with the 5D3 outer point and it's settings tells me an EV of ~1.5
-2EV that the 5D3 is rated for is similiar to F1.4 - 1/15 - 12,800 which is pretty damn dark. The 6D can focus in that light at ISO 25,600 as long as there is contrasting lines.
THE MAIN THING is even though you might be in very dark an object like the flag that is reflecting light is actually a higher EV and contrasting lines. This is why your camera will focus on a lit LED from a clock in COMPLETE DARK