My site use to have no comments on the pages I did not want them, and worked fine on pages I did. Recently, all my pages have the comments turned on for them.
So, just to be clear I went back to each page, made sure in the Discussion box that the 'Allow comments' and 'Allow trackbacks and pingbacks on this page' were both un-checked then saved the page. When I viewed the pages, the 'Leave a Reply' comment section was still at the bottom of the page.
I even use them 'Select all pages from the Pages screen, use Bulk action edit and choose Do not allow comment' method, and the comment sections are still there.
I'm thinking it's an Add-on but wanted to see if anyone else has this issue?