The CPU which he has, the i7 970 has 6 cores, now those 6 cores all share the tiny amount of 4gb of ram, by increasing the ram amount, each core will be able to process more at a higher rate of speed, you may say it won't increase performance but I say otherwise.
Try this, say each core has an equal slice of the RAM to occupy in this scenario, each of the 6 cores will only have 682 MB of RAM to use, by increasing the amount of Ram to 8 GB, each core will then be able to use 1.36 GB of ram, if it happened to spread the Ram equally between all of the cores.
Not to mention the CPU also runs 12 separate threads, the more Ram, the more processing ability there is, the more data is able to be transferred across to and from the processor at a single moment thus leading to increased response time and performance hand in hand.