I have a feeling their are some loose ends in their code where a user visits Page A then navigates to Page B and posts a comment there, but Disqus wasn't properly updated and the comment therefore gets filed under Page A.
It't not really a single-page-app, we just load the next article via ajax. First page loads normally. I prototyped that out but quickly realized it was totally overkill for a publication like this.
This particular issue is actually related to migrating comments to the new domain & urls. We actually have to provide Disqus with legacy urls for old articles. A few got mixed up. The reloading is actually working just fine.