I never shot with the 5D2 so I can't say how good/bad it was. I do have the 5Dc, though. I've shot with the 7D and I know my 5D3 can outfocus my 7D and 5Dc in low-light conditions. Where the 7D/5Dc fails to lock, the 5D3 will still achieve focus (not snappy quick, but it will lock correctly). Certainly, there will come a time when it refuses to focus. But there's only so much a camera can do.
At this point, it sounds like yours is defective, but I'll test it again when I get home. I had tried in both AI servo and one-shot.
In One-shot:
1) While camera is focusing, I only see the bottom two triangles.
2) If focus is acquired and locks, the circle lights up solid and stays lit.
3) If focus could not be achieved, the circle blinks and continues to blink for as long as I have the shutter button half-pressed.
In Servo:
1) Two lower triangles will light up during focus.
2) IF the camera is unable to focus, then the circle lights up and blinks for as long as there's nothing it can focus on and that I've got the shutter button half-pressed.
If your camera tells you it's locked on something every single time when it obviously hasn't, then sounds to me like it's defective. Hard to say what kind of lighting situation you're in though. My usual low-light situation that I should comes to be roughly: 1/200s, f/1.2, iso3200.