All my lenses are f/2.8 or faster and my 6D auto focuses just fine! I just shot a Boy Scout event last weekend, mostly with my 70-200 and 135mm, the majority at 2.8 or faster and only 3 out of focus shots out of 140+, nailed all the 135L shots at f/2 to 2.4.
It's great to hear that your 6d is working fine, but imho unless your 6d has another sensor array this simply means you're lucky (or didn't look @100% crops) - with wider apertures, the 6d af is f2.8 non-cross and falls back to f5.6.
This means if you focus on a high-contrast target, you'll be fine, but you'll get some micro-misses on low-contrast surfaces, it might not occur often mind you. That being said, I cannot exclude the possibility that the 135L for some reason or another works better as the 100L is known to hunt a bit anyway, at least in low light (but that wasn't the case here).
Maybe there is something wrong with your camera?
I doubt it, but of course cannot exclude the possibility of a lens/camera problem w/o proper testing w/ another set. However looking at the amount of problematic experiences with the 5d2/6d af, the lens is afma'd and given the high af hit rate I suppose correctly so.
Here are two samples, f2.8 @ 1/4000s - in one shot there is a tiny mis-focus, i.e. another part of the shot is in focus. This is a live object and handheld so I cannot exclude the possibility of me slightly moving, but my 60d seems to be more reliable with this setup - which is to be expected since the dof is deeper on crop, but I also suspect the 6d af as a source of the problem because the misses are more often on low contrast surfaces.