Due to the modern implementation of what nVidia used to call TurboCache (a way of using system RAM as VRAM so they could market GeForce 6 cards with 16MB of VRAM as if they had 1GB) their cards appear to cache to the system RAM before hitting up the pagefile. At least that's what I've observed... with 6GB of VRAM, if I have Surround settings which max my cards out, they swap to sysRAM; if they fill that (which they do) they hit up the pagefile. With 12GB of RAM, the only two games I've seen push sysRAM usage up to crazy levels are Crysis and Metro 2033... that was back with the 460s, though - not tried it with the 680.
I don't know why, but caching VRAM contents to sysRAM isn't exactly efficient. There's a huge overhead, some of which can be written off to the fact that with SLI, the contents of VRAM are mirrored, and thus I presume that the cards can't reference the same sysRAM addresses at the same time, despite needing identical data (if it's texture memory, as they don't cache the framebuffer) and then the driver needs some extra space reserved for figuring out what is where.
Anyway, the point of this information is a fairly simple... test your RAM out. It may be possible one of the sticks has an problem, and that Starcraft is the only thing writing to that address. BF3 utilises VRAM very well from all reports. DICE appear to have done an excellent job with the new Frostbite engine; if you have the VRAM, it'll use it... if not, it won't be greedy.