So, because of the GPL, proprietary distro companies such as Red Hat can't copyright the Linux source code. Then what, exactly, do they get to copyright? Anything other than their names and mascots, logos, etc.? I don't understand this yet.

A distro company (like anyone else) holds copyright on any code/text that they originated.

Copyright is not something you do, it is an automatic legal right (you do not have to apply for it).

Anyway, I suspect what lies at the heart of your question is 'what gives a commercial distro company the ability to charge their clients'?

Primarily the answer is that the commercial distro companies are IT support organizations. They charge for professional services and support, and not for a license to use the software.

Having said that, companies like Red Hat have made major contributions to free software packages that are part of their distros, writing code, documentation, packaging, and so on. They have copyright over portions of the software, even though they release under free software licences. The free licences give clients freedom in use of the software, but they are not an assignment of copyright to the clients.

The GPL does not prevent copyright over Linux source code. Just the opposite, the copyright law is used as a way of ensuring that users retain certain freedoms. The Linux kernel does not require that contributors assign their copyright to a central group, so the copyright of the kernel is held by many parties, which includes the commercial Linux companies.

They also trademark the logos and branding ... look at CentOS, it's basically just a repackaging of RHEL without the official trademarked branding and the name Red Hat. Either way Red Hat sells supports, that's how they make money, not by selling the OS itself.

Thank you. I was getting the impression, yes, that they sell not products but service. I wasn't sure of it.