That said, the article you linked to is specifically about WordPress - defending their decision to make ALL links absolute links.
I worked on a government project (using Wordpress) that required that all URLs be relative unless absolutely necessary and we had to add a plugin to undo all of that linking.
I've been using relative links in content for many years without any trouble. It has been suggested this is a bad practice, but the reasons given I haven't found terribly convincing. I may be wrong, but it seems as though people are using relative linking as a scapegoat for generally bad practices.
The way I see it, if broken links are being deployed then testing isn't thorough enough. If a test environment is accessible to uninvolved parties (e.g. spiders) then testing isn't controlled enough. If multiple paths exist to the same content without good reason, then the architecture is poor.
Looking around Google, this seems to be rather representative of the arguments. Relative links are bad because when they're combined with other issues that should never happen the results are undesirable. That's not good enough for me. Does anybody have a better reason?