No that's not true at all. The bandwidth might be more than is necessary for the card. Excessive bandwidth won't make the card much faster.
Look at the reviews for overclocking cards out there such as the 8800GTX. Increasing memory speed gives far less performance increase than increasing the core or shaders.
The fact that ATI was able to use the same core across GDDR3 (4850) and GDDR5 (4870) suggests that the actual bandwidth needed for the processing power probably lay somewhere in between what the 4850 and 4870's bandwidths were. Doubling the processing power means it should still be fine with the memory bandwidth given
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