The only thing I think you may have gotten mixed up here is that CentOS or other clone distros didn't remove the branding. Red Hat did that themselves in thier repositories that were used in the clones.

If I'm remembering correctly, in the very early days of Centos and the like, that was the deal that Red Hat had struck...you don't use our trademarks/branding and you can have access to all of our source. Most likely so that Red Hat wouldn't get endless support tickets without pay if something went wrong on a clone package.

The rest of this seems pretty spot on.