singular.php instead of page.php

My client requested I use the Publisher templatic theme: http://ift.tt/1rFCtlC. So far, I'm less than thrilled with the architecture of their themes.

For some strange, unknown reason, they're using a singular.php for showing both posts and pages. I can't find any documentation anywhere about singular.php, except for here: http://ift.tt/1vBTr2R and it doesn't look like it's been officially added.

I've added single.php and page.php to my child theme, but they're not overriding singular.php. These themes are also not coded in such a way that I can make changes without editing some of the plugins they force you to use, therefore losing the ability to update without losing customizations.

Does anyone know about this strange set up? Any advice?