> You're exposed to claims if you use someone else's code

The article doesn't say that the author of the software is at risk if he/she shuns licensing. It say that their collaborators are at risk. Which is true. Because as you point out, "as soon as you write some code, you own the copyright."

If you were to write some code and not place it under a legitimate open source license - "shun copyright licensing altogether" as the article states - then you have placed collaborators at risk. If I were to modify that code, redistribute it, etc, then I've taken on liability and you could sue me for infringing your copyright.