Computational binding implies Perfect hiding?
This is not correct. It could be not binding since you can open a commitment into two options. You can quite easily construct such a scheme artificially. For example, take any perfectly binding scheme $C_b$ and any perfectly hiding scheme $C_h$. Then, commit to a message $m$ by committing to $C_b(m)||C_h(0)$ or by committing to $C_b(\overline{m})||C_h(1)$. Then, when you decommit, if the perfectly hiding part is 0, take the message $m$ in the perfectly binding part. In contrast, if the perfectly hiding part is 1, take the complement of the message in the perfectly binding part. 

Clearly, this is a computationally binding scheme only, since an all-powerful committer can break the binding of the perfectly hiding part, and so can recommit to either the message or its complement. In addition, the scheme is clearly only computationally hiding as well.