Problem with custom template for Wiki plugin

I've been playing with the Wiki plugin template. The idea is to copy the incsub_wiki.php to your theme's folder and modify it there.

Using the default Twenty Twelve theme, when I do this, the formatting is all screwy and the content extends outside the frame (doesn't wrap). This happens even if I just use the template file exactly as it is. It's like moving the template file from the plugin folder to the current theme folder makes things break.

A peek at the code shows this:

Working correctly (no new template)
<body class="page page-id-45 page-template-default logged-in admin-bar no-customize-support custom-background custom-font-enabled single-author">

Broken (copied template into themes folder)
<body class="single single-incsub_wiki postid-45 logged-in admin-bar no-customize-support custom-background custom-font-enabled single-author">

It might be an issue with the get_header('wiki') call at the top of the template not including the correct classes when it's called from a different folder.

Further along in the output there is a different order to the various classes and wrappers use.

Whilst you won't be able to visually see the results, you can compare these two outputs and see the differences:

Broken: http://pastebin.com/NGtfgyVn
Correct: http://pastebin.com/3ga3RMdw

Any ideas what's happening here?