Every modern CPU can do this, but they don't, unless explicitly configured to do so. We know this because it would have been news already if they do. Network activity is suspicious. And Intel ME has been with us for 16 years now!
Also, please note that the discussion is not about possibility. It was explicitly stated that "Every modern CPU does this", and here, "this" refers to "calls home with full access to your everything". Now, that is patently false.