How do I override views-view-summary-unformatted.tpl.php inside my own theme?
I know this is old but today I struggled with this and thought I should provide a solution.  

First, you have to rename your copy of 'views-view-summary-unformatted.tpl.php' so views can discover it. It should be named 'views-view-summary-unformatted--my-view.tpl.php'.  

You then need to click the 'rescan template files' button under the theme information in the view.