I have no idea why but i never had tearing on my 6970! Might be because i used DVI/DVI/DP nativ.
That cannot be it since I used DVI/DVI/native DP on my 6950 as well and had tearing.
I think it's when not all 3 are the same that you can experience tearing on some. I don't think there are any hard and fast rules about which will tear, though I could be wrong. But on my system, my 2 DVI->DVI screens tear, but my DP->MiniDP->DVI screen does not. So I put the non-tearing monitor in the center of my system so it annoys me the least.
I believe it has to do with different digital signals and that current gpu's can only send one particular kind of signal true all the ports at one time. I have done screen tearing testing on both my 6950 and 7950, both cards respond in the same manner. Whichever screen signal is set to primary (via CCC or Win) doesn't tear including the monitors that are connected via the same kind of port. So on my 6950 I had DVI/DVI/native DP and I had to set one of the DVI monitors as my primary monitor to eliminate tearing on the other monitor that was connected via DVI. On my native DP monitor I had tearing. With my 7950 it is the other way around. It is connected via miniDP/miniDP/DVI and I only have tearing on the monitor that is connected via DVI.