Not a particularly well-written article. The referenced Ars Technica article actually explains the problem:
Muse has allowed users to share searches, conversations, images, and similar content with other people. Such share features usually involve clicking an option to create a unique URL that anyone can use to load a page hosting the content. To keep potentially sensitive information from being accessible to unintended people, the URLs typically contain a long sequence of text that can’t be easily guessed.
... a central design decision for constructing URLs has made the links easy to discover. As a result, researchers from security firm Claroc said they were able to enumerate 6,800 links Muse users created for sharing conversations with others. After opening a few hundred of them, the researchers found information that was clearly not intended to be publicly available.
Claroc researchers were able to discover the Muse share links because all of them use the domain name cf.metaaiusercontent.com. Discovery is further made easy by the decision to add the conversation name to the URL, along with a long string of text... It’s this last design decision, putting the conversation title in the subdomain rather than in the URL path, that makes public discovery possible.