Phantom template file?
Ok, these elements do not display an "edit block" option when I am logged in as an admin and mouse hover them, nor do they display any of the HTML class / id properties which are typically associated with a block.  So It had to be somehow injected or modified VIA a template file.

I did however, finally discover that they were in fact being added via a cryptically named block.

This meant that it was likely being acted upon by a "block-" template. Armed with the newly discovered block number, I found that the file "block-block-22.tpl.php" was stripping the edit link and other divs and formatting to prevent the block from having it's own background etc.

The standard "block.tpl.php" file writes all blocks in the sub-theme like:

&lt;div id="block-&lt;?php print $block-&gt;module . '-' . $block-&gt;delta; ?&gt;" class="&lt;?php print $classes; ?&gt;"&gt;
    &lt;div class="block-inner"&gt;

  &lt;?php if ($block-&gt;subject): ?&gt;
    &lt;h2 class="title"&gt;&lt;span&gt;&lt;?php print $block-&gt;subject; ?&gt;&lt;/span&gt;&lt;/h2&gt;
  &lt;?php endif; ?&gt;

  &lt;div class="content"&gt;
    &lt;?php print $block-&gt;content; ?&gt;
  &lt;/div&gt;

  &lt;?php print $edit_links; ?&gt;

&lt;/div&gt;&lt;/div&gt; &lt;!-- /block-inner, /block --&gt;


Whereas "block-block-22.tpl.php" was overriding the default and writing it as such:

&lt;?php print $block-&gt;content; ?&gt;


effectively stripping all of the block's formatting so that only the images that it contained would show with no extra margin, padding, background etc. 

I had a feeling I was missing something simple... 

Furthermore, changing it to:

&lt;?php print $edit_links; ?&gt;
&lt;?php print $block-&gt;content; ?&gt;


Enabled the "edit block" link for administrators, so now it can be edited directly from the page.