I understand the quandary, but I think the actual answer does not involve nucleophilicity. I think even a poor nucleophile would succeed.
Indeed, iodide is a paradox. It is a good nucleophile and good leaving group. It would seem that chloride could also displace iodide. However, in this case it should be pointed out that sodium iodide is soluble in acetone while sodium chloride is not. Given these conditions, what effect on the reaction would a high iodide and low chloride concentration have on an SN2 reaction?