Simply put, Magento ignores the version of the redundant file lower in hierarchy and recognizes only the version higher in hierarchy for file names, and not every template from HT has all default files included. When a file in an HT theme isn’t found, Magento looks in the other template folders until it is found in the default theme (which happens immediately if there is no other template installed). In your case, since there is another template installed, Magento is falling back to the version of the lower template in hierarchy rather than the default theme, which HT themes were designed to do.
Ideally, you should find those files that are being called from the default theme and copy them into your HT template folder so Magento reads it. The link to your site is broken, so get that up and I’ll try to help out more.