I have a 6970 2GB and mine also reads, Approx. Total Memory: 755 MB
I assume their reading of the ram is just not very good.
CCC says I have 2048 MB
And System information also shows it at 2GB.
I wouldn't worry about it.
Thanks for the reply, I checked out CCC and System Info and it too says I have 1gig.
I thought there was something wrong with my card.