Feels like a silly question to ask, but I can't find a definitive answer anywhere.
My project is a multi-site that features several themes that our users can choose from. These are all installed in /sites/all/themes. For one site in particular, I wanted to simply use a different page.tpl.php file. I tried copying the theme's page.tpl.php file into /sites/my_site/themes, but this didn't seem to work. This leads me to the question:
In order to override a template, must I use a sub-theme?