Our client requires installing RHEL 6.3 in the Content Delivery Server. I would like to know if besides the support for RHEL 6.4 and RHEL 5.9, the RHEL 6.3 version is also supporting the Content Delivery Server Roles. We've read the SDL Tridion 2013 Product Prerequisites guide, but we haven't found anything about it.
The latest version of any of the supported operating systems
So for Red Hat Enterprise Linux, that will be version 6.4 (or optionally 5.9/5.10).
Version 6.3 is therefore not officially supported, as it is not a latest version. But as with any of the platform support cases, it generally means that other OS versions will work just fine (unless there is a defect affecting SDL Tridion that has been fixed in the latest release). But if you do encounter an issue and that cannot be reproduced on the current (supported) version, then you are on your own (and advised to upgrade your OS).
So since you are in the process of installing a new server anyways, I would always go with the most current release that you can get, and stay on a supported platform.