Hmmm. Looks like Red Hat may not support version 6.2 much longer. I noticed because the latest Red Hat Advisory does not include information for versions earlier than 7.1.
Red Hat's Errata page (which lists Security Alerts and Bug Fixes) still claims support for version 6.2, but the stated policy is to support the "two most recent major product releases" -- 7 and 8.
I called customer support, and they said that Red Hat Network (the up2date utility) and Errata support for 6.2 will go away "very, very soon".
So, if you're running version 6.2, and the possibility of running an OS for which security patches are no longer released scares you, you might want to upgrade.