(Prices include shipping, taxes, and discounts when available.)
There is $30 of discounts worked in there so it is $718 before rebates. If you are dead set on you budget, you can drop the case down to a Rosewill Challenger- U3, which is $50 on NewEgg. That will save you $28 and get you under $700
The 6870 would bottleneck before the i3 would. You would maybe see 1-2 FPS difference between an i3 and an i5 with a 6870 in BF3. The GPU should almost always cost twice as much, if not more than the CPU.
He is better of to go with a lower end CPU and a high end GPU. If he upgrades the CPU to an i5, the bottleneck will be passed on to the GPU. At which point he could crossfire.