if you are using the code from the thread you linked to, to disable the comments on post and pages then when a new post/page is added it should have the comments automatically disabled.
The existing posts/pages will have comments enabled unless you uncheck the “Allow comments” checkbox when editing a post.
A quick and dirty way to disable comments for all posts is to run the below MySQL query from phpMyAdmin
UPDATE wp_posts SET comment_status="closed" WHERE post_type = "post"
You can also go to wp-admin / Posts panel, check all the posts, in “Bulk Action” select “Edit” and press “Apply”, additional options will show, now in the “Comments” field select “Do not allow” and click “Update” button.