Actually, you both are wrong. Video RAM is counted into the total maximum system memory by an OS (when addressing things). It will use that 1GB of VRAM for sure, but don't expect the system to properly address 1GB of system RAM.
Wanna know why? Because a portion of system ram is ALWAYS going to be used for your graphics card, and most systems, you can adjust how much system RAM is reserved FOR the GPU, even if it is a dedicated card.