It's not consensus (yet?), but Kloekhorst's categorization does put the Anatolian split first and early, making it essentially two separate branches of PIE. He isn't concerned about the terminology, but it does allow for alternatives, and "Proto-Indo-Hittite" is now a century-old term.

Despite the terms used, Anatolian and non-Anatolian languages are seen as two separate branches.

Maybe I'm being too charitable, but I hadn't read that user's comment as a "well, acktually", especially given the chain of comments, but perhaps I'm wrong.

Everyone puts the Anatolian split first and early. It doesn't mean the use of the term "Indo-European" for the entire family, Anatolian included, is in any way superseded or unpopular among experts.