Copyright and publishing (or reproduction) rights are two different things.
Copyright is a legal term. In the UK and the USA at least, all writers automatically own full copyright in their work as soon as they create it, and laws exist to protect them.
Publishing rights are what writers sell, assign, license or otherwise hand over when they allow others to publish their work.
The distinction between the two might seem clearer if you think of publishing rights as “the right to publish”.
Writers can assign publishing or reproduction rights to their work to enable others to publish it. If someone takes a piece of work without the copyright holder’s permission, whether from the internet or anywhere else, they’re stealing publishing rights which might otherwise have been sold elsewhere. They are in breach of the writer’s copyright, and liable to be prosecuted.