You need to disable the comments for the post. This is a default WordPress setting. You do this under the “Discussion” meta box when editing a post. The theme’s option is just referring to the entire comment form area, because normally if you just disable comments, most WordPress themes will display text that says something like “Comments closed” — So the option allows you to hide that in addition to disabling comments in the standard way.
If you don’t see this meta box, it means you have it hidden. You’d just go to the “Screen Options” tab at the top of the post Edit screen and enable it.