There's no evidence that 1280MB are VRAM limited at all in BF3 or other games (let's keep Skyrim out of this thread, the vanilla game isn't limited by memory and the outdated engine is what causes poor memory management to have troubles handling 4K resolution mods).
Even in the benchmarks posted by "2GB minimum" preachers in this thread, there's absolutely no evidence whatsoever that 1.25GB is not enough for BF3.
It's simply the case of raw power that these cards carry, namely GTX 470, GTX 560 TI 448 and GTX 570, that might not produce enough framerates with Ultra preset at 1920x1080, which is clearly shown here:
I would also argue that not even a GTX580 is enough for this game, nor HD7850/70 or any lower card, with this preset and resolution. It's not a case of VRAM limitation, simply the GPU isn't powerful enough to render the game at "acceptable" framerates.
Most BF3 players are willing to put a few settings down to get the framerates to 60 avg, 45 min, as that will affect their overall experience more than higher res textures, etc.
So let me ask you this question, what framerates do you find acceptable in multiplayer games like BF3 to deem them "playable"? I know this perceived figure can vary depending on the game and person, but if we set up some standards as to what we consider playable, it will be easier to determine a cut off point where raw power of the GPU is limited by VRAM.
Because, quite frankly, simply saying that "herp 1GB VRAM is not enough derp" is just... not enough.
With all that said, multi-gpu setups are a bit of a game changer since raw power can often double in some scenarios and VRAM limits can come to effects at such times. This also means that anyone planning to go Crossfire/SLI in the future should have that point in mind, VRAM requirements aren't getting any lower and some titles might struggle to maintain desired framerate when buffered memory is not enough.
Yet again, there are cases when a game can use much more than it requires and buffering isn't always needed. The discussion should also include bus limitations and how memory bandwidth can become a deciding factor in overall enjoyment from playing a game.
And on another note, I think the 1GB vs 2GB debate can be closed as such, there's no point arguing that some games might require more than 1GB VRAM in specific scenarios. That's not to say that all of these cards have simply not enough power to run those games with such settings, regardless of VRAM size.
EDIT: and just to refer to your comment, which I meant to do in the first place,
Anandtech's Bench data shows why you experienced a jump going from a GTX470 to an HD6970. It's simply a faster card.