I spent almost two hours in 2.6.1 (installed via cPanel) looking for how to turn off comments globally, and finally found this:
Comments > Settings > Discussion
and on that page, unchecked
[ ] Allow people to post comments on the article
... and [Save Changes] at the bottom
... but then my one test message still allowed comments, and finally figured out to access it (as if I wanted to edit the message), scroll to the bottom, open up Comments & Pings, and turn of comments for that page.