This paper studies an online cost optimization problem for distributed storage and access. The goal is to dynamically create and delete copies of data objects over time at geo-distributed servers to serve access requests and minimize the total storage and network cost. We revisit a recent algorithm in the literature and show that it does not have a competitive ratio of $2$ as claimed by constructing a counterexample. We further prove that no deterministic online algorithm can achieve a competitive ratio bounded by $2$ for the general cost optimization problem. We develop an online algorithm and prove that it achieves a competitive ratio of $\max\{2, \min\{γ, 3\}\}$, where $γ$ is the max/min storage cost ratio among all servers. Examples are given to confirm the tightness of competitive analysis. We also empirically evaluate algorithms using real object access traces.