How to modify user messages without hacking core user module? When "themeing" modules, especially core modules, as far as I know it is a good idea to take the module specific tpl.php files, duplicate the ones you need, and modify them once they're in the relevant theme directory.

However, what if I want to modify a .inc file? Is it the same process as with tpl.php files, or is there a better workflow? Basically what I would like to do is change some of the user status messages found in user.admin.inc in the core Drupal 7 User module. I'm not sure if editing this file directly is a good idea. Thoughts?
You can't override an .inc file by copying it to your theme, but you can override most of the function with your template.php; for example, any form can be altered using hook_form_alter(), or any function whose name starts with "theme" can be override by using  YOURTHEME_functionaname() in your theme template.php.