This is most peculiar... I whipped up a simple template with just a "hello" QAT button from the template. Deriving documents from it do not duplicate this button. It's unclear to me why my "real life" file does duplicate the buttons... Anyway, the simple template is included. Double clicking it opens a new document based on the template.
(For odd reasons I could not upload it as SimpleTemplate.dotm (as it is a template) but only as a .docm - so you need to rename this if downloaded)