If I had a decent thought on why, you know I would voice them (judging from your salty opinion of my posts). Your guesses are solid though. I mean, obviously, the 6950 is a more powerful card so logic would take me in the direction you have already went as far as texture units/fill rates, since it appears memory capacity, especially at lower resolutions appears to have a negligable affect if any at all.
Truth be told, I do not know a lot of how these cards tick. I just knew what you stated was contrary to others that have reviewed the same subject as I have read up on them. You asked for proof, and I provided it.
EDIT: Its also possible that the test was bunk. Are your results repeatable? Did you only test once and record the result or did you take a sample of results and discard the anomolous ones (lowest/highest results). When I/staff here review GPU's we make at least 3 runs to make sure a single results isnt anomolous.
EDIT2: Onus is on you, as the person providing the results, to also provide the answers/support of your results.
EDIT3: Ok last edit
p)... Your testing is awesome and trust me I KNOW how much effort goes in to getting results like this. The only item I questioned was the 2GB of ram making the difference at a relatively low resolution.
EDIT4: After some crtical thinking, see if you can clock up the memory speeds on the 6850 to match the 6950. That will give you a pretty decent idea on if its bandwidth limited between the two cards... If it doesnt change much, chances are bandwidth has little to do with it, If the results change dramatically, chances are it is a bandwidth thing. Im a betting man and I believe that AA uses memory bandiwidth more so than textures. I would crank the AA to 16x on both cards to stress the heck out of them and then overclock the memory on the 6850 and see what happens.