A couple of questions
You posted "If you are talking about the Layout Settings under the Configuration menu, there is no such setting for this template."
But I do, see picture below - is this a problem for me that I have this setting?
I can't tell you if there is a problem because you are not using the responsive_classic template. You are apparently trying to take portions of it into another template. The other template is what is causing the setting you see in Layout Settings. Stock responsive_classic does not have an "on/off switch" for the responsive portion of the template.
I'd be interested in knowing where the template came from that you are using.
Attachment 19116

What do you mean by columns? Are you talking about the sideboxes are (or) entire columns on either side? All of that can be done without editing a file.
The global (complete) turn off of the left and right columns is done in the Layout Settings menu. That turns either column off throughout the site. So, if the goal is no left or right column on any page, the answer is not in a file but the Layout Settings.
Attachment 19117

The only time it is recommended to use the tpl_main_page.php method is if you need to turn them off on one or two pages.

You didn't make it clear if you wanted them gone completely or just on a few pages.