Not exactly. They don't have the exact same parts. When fabricated, the different GPUs and RAM chips (among everything else) get tested for quality - I don't know how exactly this is done. They are then binned based on quality. Top parts go to the 6970, worse parts to the 6950. So the physical parts might simply not accept 6970 voltages, timings, and speeds, period.
After all look at any GPU overclocking and you'll see very few people are able to hit the same GPU and mem clocks.